∀ {α : Type u_1} [inst : CompleteLattice α] {s : α} (parts parts_1 : Set α) (e_parts : parts = parts_1)
  (sSupIndep' : sSupIndep parts) (bot_notMem' : ⊥ ∉ parts) (sSup_eq' : sSup parts = s),
  { parts := parts, sSupIndep' := sSupIndep', bot_notMem' := bot_notMem', sSup_eq' := sSup_eq' } =
    { parts := parts_1, sSupIndep' := ⋯, bot_notMem' := ⋯, sSup_eq' := ⋯ }