/usr/share/hol88-2.02.19940316/Library/window/thms.ml is in hol88-library-source 2.02.19940316-15.
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% Copyright (c) Jim Grundy 1992 %
% All rights reserved %
% %
% Jim Grundy, hereafter referred to as `the Author', retains the %
% copyright and all other legal rights to the Software contained in %
% this file, hereafter referred to as `the Software'. %
% %
% The Software is made available free of charge on an `as is' basis. %
% No guarantee, either express or implied, of maintenance, reliability, %
% merchantability or suitability for any purpose is made by the Author. %
% %
% The user is granted the right to make personal or internal use %
% of the Software provided that both: %
% 1. The Software is not used for commercial gain. %
% 2. The user shall not hold the Author liable for any consequences %
% arising from use of the Software. %
% %
% The user is granted the right to further distribute the Software %
% provided that both: %
% 1. The Software and this statement of rights is not modified. %
% 2. The Software does not form part or the whole of a system %
% distributed for commercial gain. %
% %
% The user is granted the right to modify the Software for personal or %
% internal use provided that all of the following conditions are %
% observed: %
% 1. The user does not distribute the modified software. %
% 2. The modified software is not used for commercial gain. %
% 3. The Author retains all rights to the modified software. %
% %
% Anyone seeking a licence to use this software for commercial purposes %
% is invited to contact the Author. %
% --------------------------------------------------------------------- %
%============================================================================%
% CONTENTS: miscelaneous theorems %
%============================================================================%
%$Id: thms.ml,v 3.1 1993/12/07 14:15:19 jg Exp $%
let PMI_DEF = definition (`win`) `PMI_DEF`;;
% |- !x. x ==> x %
let IMP_REFL_THM =
prove
(
"!x. x ==> x"
,
GEN_TAC THEN
DISCH_TAC THEN
(ASM_REWRITE_TAC [])
) ;;
% |- !x y z. (x ==> y) /\ (y ==> z) ==> x ==> z %
let IMP_TRANS_THM =
prove
(
"!x y z. ((x ==> y) /\ (y ==> z)) ==> (x ==> z)"
,
(REPEAT GEN_TAC) THEN
(BOOL_CASES_TAC "x:bool") THEN
(BOOL_CASES_TAC "y:bool") THEN
(REWRITE_TAC [])
);;
% |- !x. x <== x %
let PMI_REFL_THM =
prove
(
"!x. x <== x"
,
GEN_TAC THEN
(REWRITE_TAC [PMI_DEF]) THEN
DISCH_TAC THEN
(ASM_REWRITE_TAC [])
);;
% |- !x y z. x <== y /\ y <== z ==> x <== z %
let PMI_TRANS_THM =
prove
(
"!x y z. ((x <==y) /\ (y <== z)) ==> (x <== z)"
,
(REPEAT GEN_TAC) THEN
(BOOL_CASES_TAC "x:bool") THEN
(BOOL_CASES_TAC "y:bool") THEN
(REWRITE_TAC [PMI_DEF])
);;
|