fact stringlengths 7 3.87k | type stringclasses 24 values | library stringclasses 13 values | imports listlengths 0 72 | filename stringclasses 416 values | symbolic_name stringlengths 1 67 | docstring stringclasses 596 values |
|---|---|---|---|---|---|---|
red_ws_cumul_pb_left {pb Γ} {t u v} :
Σ ;;; Γ ⊢ t ⇝ u -> Σ ;;; Γ ⊢ u ≤[pb] v -> Σ ;;; Γ ⊢ t ≤[pb] v. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | red_ws_cumul_pb_left | null |
red_ws_cumul_pb_right {pb Γ t u v} :
Σ ;;; Γ ⊢ t ⇝ u -> Σ ;;; Γ ⊢ v ≤[pb] u -> Σ ;;; Γ ⊢ v ≤[pb] t. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | red_ws_cumul_pb_right | null |
red_ws_cumul_pb {pb Γ t u} :
Σ ;;; Γ ⊢ t ⇝ u -> Σ ;;; Γ ⊢ t ≤[pb] u. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | red_ws_cumul_pb | From well-typed to simply well-scoped equality. |
red_ws_cumul_pb_inv {pb Γ t u} :
Σ ;;; Γ ⊢ t ⇝ u ->
Σ ;;; Γ ⊢ u ≤[pb] t. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | red_ws_cumul_pb_inv | null |
conv_cum {cf:checker_flags} pb Σ Γ T T' :=
Σ ;;; Γ |- T <=[pb] T'. | Definition | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | conv_cum | null |
ws_decl Γ d := (on_free_vars_decl (shiftnP #|Γ| xpred0) d). | Notation | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_decl | null |
open_decl (Γ : context) := { d : context_decl | ws_decl Γ d }. | Definition | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | open_decl | null |
open_decl_proj {Γ : context} (d : open_decl Γ) := proj1_sig d. | Definition | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | open_decl_proj | null |
vass_open_decl {Γ : closed_context} (na : binder_annot name) (t : open_term Γ) : open_decl Γ :=
exist (vass na t) (proj2_sig t). | Definition | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | vass_open_decl | null |
ws_cumul_decls {cf : checker_flags} (pb : conv_pb) (Σ : global_env_ext)
(Γ : context) (d : context_decl) (d' : context_decl) :=
All_decls_alpha_pb pb (fun pb => @ws_cumul_pb cf pb Σ Γ) d d'. | Definition | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_decls | null |
ws_cumul_decls_wf_decl_left {cf} {pb} {Σ} {wfΣ : wf Σ} {Γ d d'} :
ws_cumul_decls pb Σ Γ d d' -> ws_decl Γ d. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_decls_wf_decl_left | null |
ws_cumul_decls_wf_decl_right {cf} {pb} {Σ} {wfΣ : wf Σ} {Γ d d'} :
ws_cumul_decls pb Σ Γ d d' -> ws_decl Γ d'. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_decls_wf_decl_right | null |
ws_cumul_decls_cumul_pb_decls {cf : checker_flags} (pb : conv_pb) {Σ : global_env_ext} {wfΣ : wf Σ}
{Γ Γ' : context} {d d'} :
ws_cumul_decls pb Σ Γ d d' ->
cumul_pb_decls cumulAlgo_gen pb Σ Γ Γ' d d'. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_decls_cumul_pb_decls | null |
into_ws_cumul_decls {cf : checker_flags} {pb : conv_pb} {Σ : global_env_ext} {wfΣ : wf Σ}
(Γ Γ' : context) d d' :
cumul_pb_decls cumulAlgo_gen pb Σ Γ Γ' d d' ->
on_free_vars_ctx xpred0 Γ ->
on_free_vars_ctx xpred0 Γ' ->
is_open_decl Γ d ->
is_open_decl Γ d' ->
ws_cumul_decls pb Σ Γ d d'. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | into_ws_cumul_decls | null |
ws_cumul_decls_inv {cf} (pb : conv_pb) {Σ : global_env_ext} {wfΣ : wf Σ}
{Γ Γ' : context} {d d'} :
ws_cumul_decls pb Σ Γ d d' ->
[× on_free_vars_ctx xpred0 Γ, is_open_decl Γ d, is_open_decl Γ d' & cumul_pb_decls cumulAlgo_gen pb Σ Γ Γ' d d']. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_decls_inv | null |
#[global]
Instance ws_cumul_decls_trans {cf : checker_flags} {pb} {Σ : global_env_ext} {wfΣ : wf Σ} {Γ : context} :
Transitive (ws_cumul_decls pb Σ Γ). | Instance | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_decls_trans | null |
wt_cumul_pb_decls {cf : checker_flags} (pb : conv_pb) (Σ : global_env_ext) (Γ Γ' : context) : context_decl -> context_decl -> Type :=
| wt_cumul_pb_vass {na na' : binder_annot name} {T T' : term} :
lift_typing typing Σ Γ (j_vass na T) ->
lift_typing typing Σ Γ' (j_vass na' T') ->
eq_binder_annot na na' ->
conv_cum pb Σ Γ T T' ->
wt_cumul_pb_decls pb Σ Γ Γ' (vass na T) (vass na' T')
| wt_cumul_pb_vdef {na na' : binder_annot name} {b b' T T'} :
lift_typing typing Σ Γ (j_vdef na b T) ->
lift_typing typing Σ Γ' (j_vdef na' b' T') ->
eq_binder_annot na na' ->
Σ ;;; Γ |- b = b' ->
conv_cum pb Σ Γ T T' ->
wt_cumul_pb_decls pb Σ Γ Γ' (vdef na b T) (vdef na' b' T'). | Inductive | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | wt_cumul_pb_decls | null |
ws_cumul_ctx_pb {cf:checker_flags} (pb : conv_pb) (Σ : global_env_ext) (Γ Γ' : context) :=
All2_fold (fun Γ Γ' => ws_cumul_decls pb Σ Γ) Γ Γ'. | Definition | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_ctx_pb | null |
ws_cumul_ctx_pb_closed_right {cf:checker_flags} {pb : conv_pb} {Σ} {wfΣ : wf Σ} {Γ Γ'}:
ws_cumul_ctx_pb pb Σ Γ Γ' -> is_closed_context Γ'. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_ctx_pb_closed_right | null |
ws_cumul_ctx_pb_closed_left {cf:checker_flags} {pb : conv_pb} {Σ} {wfΣ : wf Σ} {Γ Γ'}:
ws_cumul_ctx_pb pb Σ Γ Γ' -> is_closed_context Γ. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_ctx_pb_closed_left | null |
wt_cumul_ctx_pb {cf:checker_flags} (pb : conv_pb) (Σ : global_env_ext) :=
All2_fold (wt_cumul_pb_decls pb Σ). | Definition | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | wt_cumul_ctx_pb | null |
wt_cumul_context Σ := (wt_cumul_ctx_pb Cumul Σ). | Notation | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | wt_cumul_context | null |
wt_conv_context Σ := (wt_cumul_ctx_pb Conv Σ). | Notation | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | wt_conv_context | null |
wf_local_All_fold Γ :
wf_local Σ Γ <~>
All_fold (fun Γ decl => lift_typing typing Σ Γ (j_decl decl)) Γ. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | wf_local_All_fold | null |
wt_cumul_ctx_pb_forget {pb} {Γ Γ' : context} :
wt_cumul_ctx_pb pb Σ Γ Γ' ->
[× wf_local Σ Γ, wf_local Σ Γ' & cumul_pb_context cumulAlgo_gen pb Σ Γ Γ']. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | wt_cumul_ctx_pb_forget | null |
into_wt_cumul_ctx_pb {pb} {Γ Γ' : context} :
wf_local Σ Γ -> wf_local Σ Γ' ->
cumul_pb_context cumulAlgo_gen pb Σ Γ Γ' ->
wt_cumul_ctx_pb pb Σ Γ Γ'. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | into_wt_cumul_ctx_pb | null |
wt_ws_ws_cumul_ctx_pb {pb} {Γ Γ' : context} :
wt_cumul_ctx_pb pb Σ Γ Γ' ->
ws_cumul_ctx_pb pb Σ Γ Γ'. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | wt_ws_ws_cumul_ctx_pb | null |
ws_cumul_ctx_pb_inv {pb} {Γ Γ' : context} :
ws_cumul_ctx_pb pb Σ Γ Γ' ->
[× on_free_vars_ctx xpred0 Γ, on_free_vars_ctx xpred0 Γ' & cumul_pb_context cumulAlgo_gen pb Σ Γ Γ']. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_ctx_pb_inv | null |
#[global]
Instance ws_cumul_decls_sym Γ : Symmetric (ws_cumul_decls Conv Σ Γ). | Instance | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_decls_sym | null |
ws_cumul_ctx_pb_forget {pb Γ Γ'} :
ws_cumul_ctx_pb pb Σ Γ Γ' -> cumul_pb_context cumulAlgo_gen pb Σ Γ Γ'. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_ctx_pb_forget | null |
ws_cumul_ctx_pb_refl pb Γ : is_closed_context Γ -> ws_cumul_ctx_pb pb Σ Γ Γ. | Lemma | pcuic | [
"PCUICCumulativity",
"PCUICWeakeningTyp",
"PCUICLiftSubst",
"PCUICRedTypeIrrelevance",
"CMorphisms",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"CRelationClasses",
"PCUICClosedTyp",
"PCUICConfluence",
"PCUICUnivSubstitutionConv",
"PCUICParall... | pcuic/theories/PCUICWellScopedCumulativity.v | ws_cumul_ctx_pb_refl | null |
wf_cases_decl d :=
wf_cases d.(decl_type) && option_default wf_cases d.(decl_body) true. | Definition | pcuic | [] | pcuic/theories/PCUICWfCases.v | wf_cases_decl | null |
wf_cases_ctx ctx :=
forallb wf_cases_decl ctx. | Definition | pcuic | [] | pcuic/theories/PCUICWfCases.v | wf_cases_ctx | null |
rename_wf_predicateb mdecl idecl p f :
wf_predicateb mdecl idecl (rename_predicate rename f p) = wf_predicateb mdecl idecl p. | Lemma | pcuic | [] | pcuic/theories/PCUICWfCases.v | rename_wf_predicateb | null |
map_branch_wf_branchb cdecl b f :
wf_branchb cdecl (map_branch f b) = wf_branchb cdecl b. | Lemma | pcuic | [] | pcuic/theories/PCUICWfCases.v | map_branch_wf_branchb | null |
forallb2_impl {A B} (p q : A -> B -> bool) l l' :
(forall x y, p x y -> q x y) ->
forallb2 p l l' -> forallb2 q l l'. | Lemma | pcuic | [] | pcuic/theories/PCUICWfCases.v | forallb2_impl | null |
forallb2_ext {A B} (p q : A -> B -> bool) l l' :
(forall x y, p x y = q x y) ->
forallb2 p l l' = forallb2 q l l'. | Lemma | pcuic | [] | pcuic/theories/PCUICWfCases.v | forallb2_ext | null |
forallb2_map_r {A B C} (p : A -> B -> bool) f l (l' : list C) :
forallb2 p l (map f l') = forallb2 (fun x y => p x (f y)) l l'. | Lemma | pcuic | [] | pcuic/theories/PCUICWfCases.v | forallb2_map_r | null |
rename_wf_branchesb idecl brs (f : branch term -> term -> term) :
wf_branchesb idecl (map (fun br => map_branch (f br) br) brs) = wf_branchesb idecl brs. | Lemma | pcuic | [] | pcuic/theories/PCUICWfCases.v | rename_wf_branchesb | null |
wf_cases_rename Σ f t : wf_cases Σ (rename f t) = wf_cases Σ t. | Lemma | pcuic | [] | pcuic/theories/PCUICWfCases.v | wf_cases_rename | null |
wf_cases_fix_context Σ mfix :
forallb (fun d : def term => wf_cases Σ (dtype d) && wf_cases Σ (dbody d))
mfix ->
wf_cases_ctx Σ (fix_context mfix). | Lemma | pcuic | [] | pcuic/theories/PCUICWfCases.v | wf_cases_fix_context | null |
test_primu_mapu {term term'} pu pt fu (ft : term -> term') p :
test_primu pu pt (mapu_prim fu ft p) =
test_primu (pu ∘ fu) (pt ∘ ft) p. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | test_primu_mapu | null |
test_primu_primProp {term} P pu (pt : term -> bool) pu' (pt' : term -> bool) p :
tPrimProp P p ->
(forall x, pu x = pu' x) ->
(forall x, P x -> pt x = pt' x) ->
test_primu pu pt p = test_primu pu' pt' p. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | test_primu_primProp | null |
wf_sort_type0 Σ : wf_sort Σ Sort.type0. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_sort_type0 | null |
wf_sort_type1 Σ : wf_sort Σ Sort.type1. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_sort_type1 | null |
wf_sort_super {Σ u} : wf_sort Σ u -> wf_sort Σ (Sort.super u). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_sort_super | null |
wf_sort_sup {Σ u u'} : wf_sort Σ u -> wf_sort Σ u' ->
wf_sort Σ (Sort.sup u u'). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_sort_sup | null |
wf_sort_product {Σ s s'} : wf_sort Σ s -> wf_sort Σ s' ->
wf_sort Σ (Sort.sort_of_product s s'). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_sort_product | null |
wf_levelb Σ l :=
LevelSet.mem l (global_ext_levels Σ). | Definition | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_levelb | null |
wf_level Σ l :=
LevelSet.In l (global_ext_levels Σ). | Definition | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_level | null |
wf_instance Σ u :=
Forall (wf_level Σ) u. | Definition | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_instance | null |
wf_instanceb Σ u :=
forallb (wf_levelb Σ) u. | Definition | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_instanceb | null |
wf_levelP {Σ l} : reflect (wf_level Σ l) (wf_levelb Σ l). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_levelP | null |
wf_instanceP {Σ u} : reflect (wf_instance Σ u) (wf_instanceb Σ u). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_instanceP | null |
wf_universe_subst_instance_univ (Σ : global_env_ext) univs ui u :
wf Σ ->
wf_universe Σ u ->
wf_instance (Σ.1, univs) ui ->
wf_universe (Σ.1, univs) (subst_instance ui u). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universe_subst_instance_univ | null |
wf_sort_subst_instance_sort (Σ : global_env_ext) univs u s :
wf Σ ->
wf_sort Σ s ->
wf_instance (Σ.1, univs) u ->
wf_sort (Σ.1, univs) (subst_instance u s). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_sort_subst_instance_sort | null |
wf_sort_instantiate Σ univs s u φ :
wf Σ ->
wf_sort (Σ, univs) s ->
wf_instance (Σ, φ) u ->
wf_sort (Σ, φ) (subst_instance_sort u s). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_sort_instantiate | null |
subst_instance_empty u :
forallb (fun x => ~~ Level.is_var x) u ->
subst_instance [] u = u. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | subst_instance_empty | null |
wf_level_mono Σ u :
wf Σ ->
on_udecl_prop Σ (Monomorphic_ctx) ->
Forall (wf_level (Σ, Monomorphic_ctx)) u ->
forallb (fun x => ~~ Level.is_var x) u. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_level_mono | null |
wf_level_sub Σ univs u :
wf_level (Σ, Monomorphic_ctx) u ->
wf_level (Σ, univs) u. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_level_sub | null |
wf_instance_sub Σ univs u :
wf_instance (Σ, Monomorphic_ctx) u ->
wf_instance (Σ, univs) u. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_instance_sub | null |
In_Level_global_ext_poly s Σ cst :
LS.In (Level.level s) (global_ext_levels (Σ, Polymorphic_ctx cst)) ->
LS.In (Level.level s) (global_levels Σ). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | In_Level_global_ext_poly | null |
Forall_In (A : Type) (P : A -> Prop) (l : list A) :
Forall P l -> (forall x : A, In x l -> P x). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | Forall_In | null |
wf_instance_In {Σ u} : wf_instance Σ u <->
(forall l, In l u -> LS.In l (global_ext_levels Σ)). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_instance_In | null |
in_subst_instance l u u' :
In l (subst_instance u u') ->
In l u \/ In l u' \/ l = Level.lzero. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | in_subst_instance | null |
wf_instance_subst_instance Σ univs u u' φ :
wf Σ ->
on_udecl_prop Σ univs ->
wf_instance (Σ, univs) u' ->
wf_instance (Σ, φ) u ->
wf_instance (Σ, φ) (subst_instance u u'). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_instance_subst_instance | null |
wf_universeb (u : Universe.t) : bool :=
LevelExprSet.for_all (fun l => LevelSet.mem (LevelExpr.get_level l) (global_ext_levels Σ)) u. | Definition | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universeb | null |
wf_universe_reflect {u : Universe.t} :
reflect (wf_universe Σ u) (wf_universeb u). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universe_reflect | null |
on_universes fu fc t :=
match t with
| tSort s => Sort.on_sort fu true s
| tApp t u
| tProd _ t u
| tLambda _ t u => on_universes fu fc t && on_universes fu fc u
| tCase _ p c brs =>
[&&
forallb fu (map Universe.make' p.(puinst)) ,
forallb (on_universes fu fc) p.(pparams) ,
test_context (fc #|p.(puinst)|) p.(pcontext) ,
on_universes fu fc p.(preturn) ,
on_universes fu fc c &
forallb (test_branch (fc #|p.(puinst)|) (on_universes fu fc)) brs ]
| tLetIn _ t t' u =>
[&& on_universes fu fc t , on_universes fu fc t' & on_universes fu fc u]
| tProj _ t => on_universes fu fc t
| tFix mfix _ | tCoFix mfix _ =>
forallb (fun d => on_universes fu fc d.(dtype) && on_universes fu fc d.(dbody)) mfix
| tConst _ u | tInd _ u | tConstruct _ _ u =>
forallb fu (map Universe.make' u)
| tEvar _ args => forallb (on_universes fu fc) args
| tPrim p => test_primu (fun x => fu (Universe.make' x)) (on_universes fu fc) p
| _ => true
end. | Fixpoint | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | on_universes | null |
wf_universes t := on_universes wf_universeb closedu t. | Definition | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes | null |
wf_sortb s := Sort.on_sort wf_universeb true s. | Definition | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_sortb | null |
wf_sort_reflect {s : sort} :
reflect (wf_sort Σ s) (wf_sortb s). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_sort_reflect | null |
wf_universeb_instance_forall u :
forallb wf_universeb (map Universe.make' u) = wf_instanceb Σ u. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universeb_instance_forall | null |
test_context_mapi (p : term -> bool) f (ctx : context) k :
test_context p (mapi_context (shiftf f k) ctx) = test_context_k (fun k => p ∘ f k) k ctx. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | test_context_mapi | null |
test_context_k_ctx (p : term -> bool) (ctx : context) k :
test_context p ctx = test_context_k (fun k => p) k ctx. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | test_context_k_ctx | null |
on_universes_lift pu pc n k t : on_universes pu pc (lift n k t) = on_universes pu pc t. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | on_universes_lift | null |
wf_universes_lift n k t : wf_universes (lift n k t) = wf_universes t. | Corollary | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes_lift | null |
on_universes_subst s k pu pc t :
All (on_universes pu pc) s ->
on_universes pu pc (subst s k t) = on_universes pu pc t. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | on_universes_subst | null |
wf_universes_subst s k t :
All wf_universes s ->
wf_universes (subst s k t) = wf_universes t. | Corollary | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes_subst | null |
to_prop :=
repeat match goal with
| [ H: is_true (?x && ?y) |- _ ] =>
let x := fresh in let y := fresh in move/andP: H; move=> [x y]; rewrite ?x ?y; simpl
end. | Ltac | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | to_prop | null |
to_wfu :=
repeat match goal with
| [ H: is_true (wf_universeb _ ?x) |- _ ] => apply (elimT (@wf_universe_reflect _ x)) in H
| [ |- is_true (wf_universeb _ ?x) ] => apply (introT (@wf_universe_reflect _ x))
| [ H: is_true (Sort.on_sort (wf_universeb _) _ ?x) |- _ ] => apply (elimT (@wf_sort_reflect _ x)) in H
| [ |- is_true (Sort.on_sort (wf_universeb _) _ ?x) ] => apply (introT (@wf_sort_reflect _ x))
| [ H: is_true (wf_sortb _ ?x) |- _ ] => apply (elimT (@wf_sort_reflect _ x)) in H
| [ |- is_true (wf_sortb _ ?x) ] => apply (introT (@wf_sort_reflect _ x))
end. | Ltac | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | to_wfu | null |
wf_universes_inst {Σ : global_env_ext} univs t u :
wf Σ ->
on_udecl_prop Σ.1 univs ->
wf_instance Σ u ->
wf_universes (Σ.1, univs) t ->
wf_universes Σ (subst_instance u t). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes_inst | null |
weaken_wf_universe Σ Σ' t : wf Σ' -> extends Σ.1 Σ' ->
wf_universe Σ t ->
wf_universe (Σ', Σ.2) t. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | weaken_wf_universe | null |
weaken_wf_level {Σ : global_env_ext} Σ' t : wf Σ -> wf Σ' -> extends Σ Σ' ->
wf_level Σ t ->
wf_level (Σ', Σ.2) t. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | weaken_wf_level | null |
weaken_wf_instance {Σ : global_env_ext} Σ' t : wf Σ -> wf Σ' -> extends Σ.1 Σ' ->
wf_instance Σ t ->
wf_instance (Σ', Σ.2) t. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | weaken_wf_instance | null |
test_primu_test_primu_tPrimProp {P : term -> Type} {pu put} {pu' : Level.t -> bool} {put' : term -> bool} p :
tPrimProp P p -> test_primu pu put p ->
(forall u, pu u -> pu' u) ->
(forall t, P t -> put t -> put' t) ->
test_primu pu' put' p. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | test_primu_test_primu_tPrimProp | null |
weaken_wf_universes {Σ : global_env_ext} Σ' t : wf Σ -> wf Σ' -> extends Σ.1 Σ' ->
wf_universes Σ t ->
wf_universes (Σ', Σ.2) t. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | weaken_wf_universes | null |
wf_universes_weaken_full :
weaken_env_prop_full cumulSpec0 (lift_typing typing)
(fun Σ _ t T => wf_universes Σ t && wf_universes Σ T). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes_weaken_full | null |
wf_universes_weaken :
weaken_env_prop cumulSpec0 (lift_typing typing)
(fun Σ _ j => option_default (wf_universes Σ) (j_term j) true && wf_universes Σ (j_typ j) && option_default (wf_sortb Σ) (j_univ j) true). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes_weaken | null |
wf_universes_inds Σ mind u bodies :
wf_instance Σ u ->
All (fun t : term => wf_universes Σ t) (inds mind u bodies). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes_inds | null |
wf_universes_mkApps Σ f args :
wf_universes Σ (mkApps f args) = wf_universes Σ f && forallb (wf_universes Σ) args. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes_mkApps | null |
type_local_ctx_wf Σ Γ Δ s : type_local_ctx (fun Σ _ => lift_wf_term (fun t => wf_universes Σ t)) Σ Γ Δ s ->
All (fun d => option_default (wf_universes Σ) (decl_body d) true && wf_universes Σ (decl_type d)) Δ. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | type_local_ctx_wf | null |
consistent_instance_ext_wf Σ univs u : consistent_instance_ext Σ univs u ->
wf_instance Σ u. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | consistent_instance_ext_wf | null |
specIH :=
repeat match goal with
| [ H : on_udecl _ _, H' : on_udecl _ _ -> _ |- _ ] => specialize (H' H)
end. | Ltac | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | specIH | null |
wf_universes_local_ctx_smash (Σ : global_env_ext) mdecl args sorts :
sorts_local_ctx (fun Σ _ => lift_wfbu_term (fun t => wf_universes Σ t) (wf_sortb Σ))
(Σ.1, ind_universes mdecl) (arities_context (ind_bodies mdecl),,, ind_params mdecl) args sorts ->
sorts_local_ctx (fun Σ _ => lift_wfbu_term (fun t => wf_universes Σ t) (wf_sortb Σ))
(Σ.1, ind_universes mdecl) (arities_context (ind_bodies mdecl),,, ind_params mdecl) (smash_context [] args) sorts. | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes_local_ctx_smash | null |
wf_universes_local_ctx_nth_error Σ P Pu Γ Δ s n d :
sorts_local_ctx (fun Σ _ => lift_wfbu_term (P Σ) (Pu Σ)) Σ Γ Δ s ->
nth_error Δ n = Some d ->
P Σ (decl_type d). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_universes_local_ctx_nth_error | null |
In_unfold_var x n : In x (unfold n Level.lvar) <-> exists k, k < n /\ (x = Level.lvar k). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | In_unfold_var | null |
wf_abstract_instance Σ decl :
wf_instance (Σ, decl) (abstract_instance decl). | Lemma | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_abstract_instance | null |
on_decl_universes (fu : Universe.t -> bool) (fc : nat -> term -> bool) d :=
option_default (on_universes fu fc) d.(decl_body) true &&
on_universes fu fc d.(decl_type). | Definition | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | on_decl_universes | null |
wf_decl_universes Σ := on_decl_universes (wf_universeb Σ) closedu. | Definition | pcuic | [
"PCUICWeakeningTyp",
"PCUICCumulativity",
"PCUICLiftSubst",
"Equations",
"ssrbool",
"DepElim",
"utils",
"PCUICSigmaCalculus",
"PCUICSubstitution",
"PCUICUnivSubstitutionConv",
"PCUICTyping",
"PCUICCases",
"PCUICWeakeningConv",
"PCUICAst",
"Stdlib",
"PCUICAstUtils",
"PCUICGeneration",... | pcuic/theories/PCUICWfUniverses.v | wf_decl_universes | null |
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