30 lines
951 B
Text
30 lines
951 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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namespace smt
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universes u v
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def array (α : Type u) (β : Type v) := α → β
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variables {α : Type u} {β : Type v}
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open tactic
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def select (a : array α β) (i : α) : β :=
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a i
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lemma arrayext (a₁ a₂ : array α β) : (∀ i, select a₁ i = select a₂ i) → a₁ = a₂ :=
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funext
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variable [decidable_eq α]
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def store (a : array α β) (i : α) (v : β) : array α β :=
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λ j, if j = i then v else select a j
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@[simp] lemma select_store (a : array α β) (i : α) (v : β) : select (store a i v) i = v :=
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by unfold smt.store smt.select; dsimp; rewrite if_pos; reflexivity
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@[simp] lemma select_store_ne (a : array α β) (i j : α) (v : β) : j ≠ i → select (store a i v) j = select a j :=
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by intros; unfold smt.store smt.select; dsimp; rewrite if_neg; assumption
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end smt
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