36 lines
976 B
Text
36 lines
976 B
Text
/-
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Copyright (c) 2016 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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prelude
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import init.data.nat.basic
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open nat
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structure fin (n : nat) := (val : nat) (is_lt : val < n)
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namespace fin
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variable {n : nat}
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lemma eq_of_veq : ∀ {i j : fin n}, (val i) = (val j) → i = j
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| ⟨iv, ilt₁⟩ ⟨.iv, ilt₂⟩ rfl := rfl
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lemma veq_of_eq : ∀ {i j : fin n}, i = j → (val i) = (val j)
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| ⟨iv, ilt⟩ .⟨iv, ilt⟩ rfl := rfl
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lemma ne_of_vne {i j : fin n} (h : val i ≠ val j) : i ≠ j :=
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λ h', absurd (veq_of_eq h') h
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lemma vne_of_ne {i j : fin n} (h : i ≠ j) : val i ≠ val j :=
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λ h', absurd (eq_of_veq h') h
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end fin
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open fin
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instance (n : nat) : decidable_eq (fin n)
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| ⟨ival, ilt⟩ ⟨jval, jlt⟩ :=
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match nat.decidable_eq ival jval with
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| is_true h₁ := is_true (eq_of_veq h₁)
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| is_false h₁ := is_false (λ h₂, absurd (veq_of_eq h₂) h₁)
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end
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