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Update minimal.lean
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erdOne authored Oct 16, 2022
1 parent c54d48d commit 17bc5cd
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions src/order/minimal.lean
Original file line number Diff line number Diff line change
Expand Up @@ -141,7 +141,7 @@ begin
end

lemma image_maximals {α β : Type*} {r : α → α → Prop} {s : β → β → Prop} (f : α → β)
(t : set α) (h₁ : ∀ x y ∈ t, r x y ↔ s (f x) (f y)) (h₂ : t.inj_on f) :
(t : set α) (h₁ : ∀ x y ∈ t, r x y ↔ s (f x) (f y)) :
f '' maximals r t = maximals s (f '' t) :=
begin
ext,
Expand All @@ -157,13 +157,13 @@ begin
end

lemma image_minimals {α β : Type*} {r : α → α → Prop} {s : β → β → Prop} (f : α → β)
(t : set α) (h₁ : ∀ x y ∈ t, r x y ↔ s (f x) (f y)) (h₂ : t.inj_on f) :
(t : set α) (h₁ : ∀ x y ∈ t, r x y ↔ s (f x) (f y)) :
f '' minimals r t = minimals s (f '' t) :=
image_maximals f t (λ x hx y hy, h₁ y hy x hx) h₂
image_maximals f t (λ x hx y hy, h₁ y hy x hx)

lemma rel_embedding.image_maximals {α β : Type*} {r : α → α → Prop} {s : β → β → Prop}
(f : r ↪r s) (t : set α) : f '' maximals r t = maximals s (f '' t) :=
image_maximals f t (λ _ _ _ _, f.map_rel_iff.symm) (λ x _ y _ e, f.injective e)
image_maximals f t (λ _ _ _ _, f.map_rel_iff.symm)

lemma rel_embedding.image_minimals {α β : Type*} {r : α → α → Prop} {s : β → β → Prop}
(f : r ↪r s) (t : set α) : f '' minimals r t = minimals s (f '' t) :=
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