∀ {α : Type u_5} {β : Type u_6} {r : α → α → Prop} {s : β → β → Prop} (toEmbedding : α ↪ β)
  (map_rel_iff' : ∀ {a b : α}, s (toEmbedding a) (toEmbedding b) ↔ r a b) (toEmbedding_1 : α ↪ β)
  (map_rel_iff'_1 : ∀ {a b : α}, s (toEmbedding_1 a) (toEmbedding_1 b) ↔ r a b),
  ({ toEmbedding := toEmbedding, map_rel_iff' := map_rel_iff' } =
      { toEmbedding := toEmbedding_1, map_rel_iff' := map_rel_iff'_1 }) =
    (toEmbedding = toEmbedding_1)