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theory ExamplesAbort(* Title: HOL/Hoare/ExamplesAbort.thy ID: $Id: ExamplesAbort.thy,v 1.5 2005/07/07 10:39:32 nipkow Exp $ Author: Tobias Nipkow Copyright 1998 TUM Some small examples for programs that may abort. *) theory ExamplesAbort imports HoareAbort begin lemma "VARS x y z::nat {y = z & z ≠ 0} z ≠ 0 -> x := y div z {x = 1}" by vcg_simp lemma "VARS a i j {k <= length a & i < k & j < k} j < length a -> a[i] := a!j {True}" apply vcg_simp done lemma "VARS (a::int list) i {True} i := 0; WHILE i < length a INV {i <= length a} DO a[i] := 7; i := i+1 OD {True}" apply vcg_simp done end
lemma
{y = z ∧ z ≠ 0} z ≠ 0 -> x := y div z {x = 1}
lemma
{k ≤ length a ∧ i < k ∧ j < k} j < length a -> i < length a -> a := a[i := a ! j] {True}
lemma
{True} i := 0; WHILE i < length a INV {i ≤ length a} DO i < length a -> a := a[i := 7]; i := i + 1 OD {True}