Use COQ proof language to solve this  (*  Prove the following spec for max. To deal with the if-then-else,    first destruct the condition, then use the tactics wp_if_true/wp_if_false    as appropriate in each case. *) Definition max : val := λ: "x" "y",   if: !"x" < !"y" then !"y" else !"x". Lemma max_spec x y (v1 v2 : Z) :   {{{ x ↦ #v1 ∗ y ↦ #v2 }}}   max #x #y   {{{ v, RET #v; ⌜v1 <= v /\ v2 <= v⌝%Z ∗ x ↦ #v1 ∗ y ↦ #v2 }}}. Proof. Admitted. End proof.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Use COQ proof language to solve this 
(*  Prove the following spec for max. To deal with the if-then-else,
   first destruct the condition, then use the tactics wp_if_true/wp_if_false
   as appropriate in each case. *)
Definition max : val := λ: "x" "y",
  if: !"x" < !"y" then !"y" else !"x".

Lemma max_spec x y (v1 v2 : Z) :
  {{{ x ↦ #v1 ∗ y ↦ #v2 }}}
  max #x #y
  {{{ v, RET #v; ⌜v1 <= v /\ v2 <= v⌝%Z ∗ x ↦ #v1 ∗ y ↦ #v2 }}}.
Proof.
Admitted.

End proof.

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