2014-12-23 20:35:06 +00:00
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/-
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Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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-/
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2014-12-01 04:34:12 +00:00
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import data.bool
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2015-01-10 22:07:20 +00:00
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open bool
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2014-07-02 15:36:05 +00:00
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2015-01-10 22:07:20 +00:00
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protected definition char.is_inhabited [instance] : inhabited char :=
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inhabited.mk (char.mk ff ff ff ff ff ff ff ff)
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2014-07-04 21:25:44 +00:00
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2015-01-10 22:07:20 +00:00
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protected definition string.is_inhabited [instance] : inhabited string :=
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inhabited.mk string.empty
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2015-05-04 03:46:33 +00:00
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open decidable
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definition decidable_eq_char [instance] : ∀ c₁ c₂ : char, decidable (c₁ = c₂) :=
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begin
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intro c₁ c₂,
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cases c₁ with a₁ a₂ a₃ a₄ a₅ a₆ a₇ a₈,
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cases c₂ with b₁ b₂ b₃ b₄ b₅ b₆ b₇ b₈,
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apply (@by_cases (a₁ = b₁)), intros,
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apply (@by_cases (a₂ = b₂)), intros,
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apply (@by_cases (a₃ = b₃)), intros,
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apply (@by_cases (a₄ = b₄)), intros,
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apply (@by_cases (a₅ = b₅)), intros,
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apply (@by_cases (a₆ = b₆)), intros,
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apply (@by_cases (a₇ = b₇)), intros,
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apply (@by_cases (a₈ = b₈)), intros,
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left, congruence, repeat assumption,
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repeat (intro n; right; intro h; injection h; refine absurd _ n; assumption)
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end
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open string
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definition decidable_eq_string [instance] : ∀ s₁ s₂ : string, decidable (s₁ = s₂)
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| empty empty := by left; reflexivity
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| empty (str c₂ r₂) := by right; contradiction
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| (str c₁ r₁) empty := by right; contradiction
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| (str c₁ r₁) (str c₂ r₂) :=
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match decidable_eq_char c₁ c₂ with
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| inl e₁ :=
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match decidable_eq_string r₁ r₂ with
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| inl e₂ := by left; congruence; repeat assumption
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| inr n₂ := by right; intro h; injection h; refine absurd _ n₂; assumption
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end
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| inr n₁ := by right; intro h; injection h; refine absurd _ n₁; assumption
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end
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