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feat(logic/quantifiers): tag congruence theorems

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Daniel Selsam 2015-11-04 21:56:35 -08:00 committed by Leonardo de Moura
parent 8e5e8e6540
commit 34f4e315ee
1 changed files with 6 additions and 3 deletions
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library/logic/quantifiers.lean
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@ -126,14 +126,17 @@ end
section section
variables {A : Type} {p₁ p₂ : A → Prop} (H : ∀ x, p₁ x ↔ p₂ x) variables {A : Type} {p₁ p₂ : A → Prop} (H : ∀ x, p₁ x ↔ p₂ x)
theorem congr_forall : (∀ x, p₁ x) ↔ (∀ x, p₂ x) := theorem congr_forall [congr] : (∀ x, p₁ x) ↔ (∀ x, p₂ x) :=
forall_congr H forall_congr H
theorem congr_exists : (∃ x, p₁ x) ↔ (∃ x, p₂ x) := theorem congr_exists [congr] : (∃ x, p₁ x) ↔ (∃ x, p₂ x) :=
exists_congr H exists_congr H
include H include H
theorem congr_exists_unique : (∃! x, p₁ x) ↔ (∃! x, p₂ x) := theorem congr_exists_unique [congr] : (∃! x, p₁ x) ↔ (∃! x, p₂ x) :=
congr_exists (λx, congr_and (H x) (congr_forall congr_exists (λx, congr_and (H x) (congr_forall
(λy, congr_imp (H y) iff.rfl))) (λy, congr_imp (H y) iff.rfl)))
end end
/- We add this attribute again here so that the simplifier finds it before [congr_forall] -/
attribute congr_imp [congr]