(* Title: HOL/Hoare/ExamplesAbort.thy ID: $Id$ 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