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feat(set_theory/zfc/basic): add refl, symm, trans attributes to…
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… `equiv` lemmas (#15549)
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vihdzp committed Jul 20, 2022
1 parent e2e097c commit 40e7791
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions src/set_theory/zfc/basic.lean
Expand Up @@ -116,7 +116,7 @@ theorem exists_equiv_right : Π {x y : pSet} (h : equiv x y) (j : y.type),
∃ i, equiv (x.func i) (y.func j)
| ⟨α, A⟩ ⟨β, B⟩ h := h.2

protected theorem equiv.refl (x) : equiv x x :=
@[refl] protected theorem equiv.refl (x) : equiv x x :=
pSet.rec_on x $ λ α A IH, ⟨λ a, ⟨a, IH a⟩, λ a, ⟨a, IH a⟩⟩

protected theorem equiv.rfl : ∀ {x}, equiv x x := equiv.refl
Expand All @@ -126,10 +126,10 @@ pSet.rec_on x $ λ α A IH y, pSet.cases_on y $ λ β B ⟨γ, Γ⟩ ⟨αβ, β
⟨λ a, let ⟨b, ab⟩ := αβ a, ⟨c, bc⟩ := βγ b in ⟨c, IH a ab bc⟩,
λ c, let ⟨b, cb⟩ := γβ c, ⟨a, ba⟩ := βα b in ⟨a, IH a ba cb⟩⟩

protected theorem equiv.symm {x y} : equiv x y → equiv y x :=
@[symm] protected theorem equiv.symm {x y} : equiv x y → equiv y x :=
(equiv.refl y).euc

protected theorem equiv.trans {x y z} (h1 : equiv x y) (h2 : equiv y z) : equiv x z :=
@[trans] protected theorem equiv.trans {x y z} (h1 : equiv x y) (h2 : equiv y z) : equiv x z :=
h1.euc h2.symm

instance setoid : setoid pSet :=
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