29 lines
935 B
Text
29 lines
935 B
Text
/-
|
|
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
|
|
Released under Apache 2.0 license as described in the file LICENSE.
|
|
Author: Leonardo de Moura
|
|
-/
|
|
namespace smt
|
|
definition array (A B : Type) := A → B
|
|
|
|
variables {A B : Type}
|
|
open tactic
|
|
|
|
definition select (a : array A B) (i : A) : B :=
|
|
a i
|
|
|
|
theorem arrayext (a₁ a₂ : array A B) : (∀ i, select a₁ i = select a₂ i) → a₁ = a₂ :=
|
|
funext
|
|
|
|
variable [decidable_eq A]
|
|
|
|
definition store (a : array A B) (i : A) (v : B) : array A B :=
|
|
λ j, if j = i then v else select a j
|
|
|
|
theorem select_store [simp] (a : array A B) (i : A) (v : B) : select (store a i v) i = v :=
|
|
by unfold [`smt.store, `smt.select] >> dsimp >> rewrite `if_pos >> reflexivity
|
|
|
|
theorem select_store_ne [simp] (a : array A B) (i j : A) (v : B) : j ≠ i → select (store a i v) j = select a j :=
|
|
by intros >> unfold [`smt.store, `smt.select] >> dsimp >> rewrite `if_neg >> assumption
|
|
|
|
end smt
|