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feat(library/data/string): prove that string and char have decidable equality

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Leonardo de Moura 2015-05-03 20:46:33 -07:00
parent 3c8c75470f
commit 3cd8f38b8d
1 changed files with 35 additions and 0 deletions
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library/data/string.lean
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@ -13,3 +13,38 @@ inhabited.mk (char.mk ff ff ff ff ff ff ff ff)
protected definition string.is_inhabited [instance] : inhabited string := protected definition string.is_inhabited [instance] : inhabited string :=
inhabited.mk string.empty inhabited.mk string.empty
open decidable
definition decidable_eq_char [instance] : ∀ c₁ c₂ : char, decidable (c₁ = c₂) :=
begin
intro c₁ c₂,
cases c₁ with a₁ a₂ a₃ a₄ a₅ a₆ a₇ a₈,
cases c₂ with b₁ b₂ b₃ b₄ b₅ b₆ b₇ b₈,
apply (@by_cases (a₁ = b₁)), intros,
apply (@by_cases (a₂ = b₂)), intros,
apply (@by_cases (a₃ = b₃)), intros,
apply (@by_cases (a₄ = b₄)), intros,
apply (@by_cases (a₅ = b₅)), intros,
apply (@by_cases (a₆ = b₆)), intros,
apply (@by_cases (a₇ = b₇)), intros,
apply (@by_cases (a₈ = b₈)), intros,
left, congruence, repeat assumption,
repeat (intro n; right; intro h; injection h; refine absurd _ n; assumption)
end
open string
definition decidable_eq_string [instance] : ∀ s₁ s₂ : string, decidable (s₁ = s₂)
| empty empty := by left; reflexivity
| empty (str c₂ r₂) := by right; contradiction
| (str c₁ r₁) empty := by right; contradiction
| (str c₁ r₁) (str c₂ r₂) :=
match decidable_eq_char c₁ c₂ with
| inl e₁ :=
match decidable_eq_string r₁ r₂ with
| inl e₂ := by left; congruence; repeat assumption
| inr n₂ := by right; intro h; injection h; refine absurd _ n₂; assumption
end
| inr n₁ := by right; intro h; injection h; refine absurd _ n₁; assumption
end