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|
(*---------------------------------------------------------------------------*)
(*
File: mk_comp_unity.ml
Description: This file proves the unity compositionality theorems and
corrollaries valid.
Author: (c) Copyright 1989-2008 by Flemming Andersen
Date: December 1, 1989
Last Update: December 30, 2007
*)
(*---------------------------------------------------------------------------*)
(*---------------------------------------------------------------------------*)
(*
Theorems
*)
(*---------------------------------------------------------------------------*)
(*
Prove:
!p q FPr GPr.
(p UNLESS q) (APPEND FPr GPr) ==> (p UNLESS q) FPr /\ (p UNLESS q) GPr
*)
let COMP_UNLESS_thm1_lemma_1 = TAC_PROOF
(([],
(`!(p:'a->bool) q FPr GPr.
(p UNLESS q) (APPEND FPr GPr) ==> (p UNLESS q) FPr /\ (p UNLESS q) GPr`)),
REPEAT GEN_TAC THEN
SPEC_TAC ((`GPr:('a->'a)list`),(`GPr:('a->'a)list`)) THEN
SPEC_TAC ((`FPr:('a->'a)list`),(`FPr:('a->'a)list`)) THEN
LIST_INDUCT_TAC THENL
[
REWRITE_TAC [UNLESS;APPEND]
;
REWRITE_TAC [APPEND] THEN
REWRITE_TAC [UNLESS] THEN
REPEAT STRIP_TAC THENL
[
ASM_REWRITE_TAC []
;
RES_TAC
;
RES_TAC]]);;
(*
Prove:
!p q FPr GPr.
(p UNLESS q) FPr /\ (p UNLESS q) GPr ==> (p UNLESS q) (APPEND FPr GPr)
*)
let COMP_UNLESS_thm1_lemma_2 = TAC_PROOF
(([],
(`!(p:'a->bool) q FPr GPr.
(p UNLESS q) FPr /\ (p UNLESS q) GPr ==> (p UNLESS q) (APPEND FPr GPr)`)),
REPEAT GEN_TAC THEN
SPEC_TAC ((`GPr:('a->'a)list`),(`GPr:('a->'a)list`)) THEN
SPEC_TAC ((`FPr:('a->'a)list`),(`FPr:('a->'a)list`)) THEN
LIST_INDUCT_TAC THENL
[
REWRITE_TAC [UNLESS;APPEND]
;
REWRITE_TAC [APPEND] THEN
REWRITE_TAC [UNLESS] THEN
REPEAT STRIP_TAC THENL
[
ASM_REWRITE_TAC []
;
RES_TAC
]]);;
(*
Prove:
!p q FPr GPr.
(p UNLESS q) (APPEND FPr GPr) = (p UNLESS q) FPr /\ (p UNLESS q) GPr
*)
let COMP_UNLESS_thm1 = prove_thm
("COMP_UNLESS_thm1",
(`!(p:'a->bool) q FPr GPr.
(p UNLESS q) (APPEND FPr GPr) <=> (p UNLESS q) FPr /\ (p UNLESS q) GPr`),
REPEAT GEN_TAC THEN
STRIP_ASSUME_TAC (IMP_ANTISYM_RULE
(SPEC_ALL COMP_UNLESS_thm1_lemma_1)
(SPEC_ALL COMP_UNLESS_thm1_lemma_2)));;
(*
Prove:
!p q FPr GPr.
(p ENSURES q) (APPEND FPr GPr) ==> (p ENSURES q) FPr /\ (p UNLESS q) GPr \/
(p ENSURES q) GPr /\ (p UNLESS q) FPr
*)
let COMP_ENSURES_thm1_lemma_1 = TAC_PROOF
(([],
(`!(p:'a->bool) q FPr GPr.
(p ENSURES q) (APPEND FPr GPr) ==> (p ENSURES q) FPr /\ (p UNLESS q) GPr \/
(p ENSURES q) GPr /\ (p UNLESS q) FPr`)),
REPEAT GEN_TAC THEN
SPEC_TAC ((`GPr:('a->'a)list`),(`GPr:('a->'a)list`)) THEN
SPEC_TAC ((`FPr:('a->'a)list`),(`FPr:('a->'a)list`)) THEN
LIST_INDUCT_TAC THENL
[
REWRITE_TAC [ENSURES;EXIST_TRANSITION;UNLESS;APPEND]
;
GEN_TAC THEN
REWRITE_TAC [ENSURES;EXIST_TRANSITION;UNLESS;APPEND] THEN
REPEAT STRIP_TAC THEN
ASM_REWRITE_TAC [] THENL
[
DISJ1_TAC THEN
ASM_REWRITE_TAC [] THEN
ASM_REWRITE_TAC [GEN_ALL (SYM (SPEC_ALL COMP_UNLESS_thm1))]
;
ASSUME_TAC (UNDISCH_ALL (SPECL
[(`((p:'a->bool) UNLESS q)(APPEND t GPr)`);
(`((p:'a->bool) EXIST_TRANSITION q)(APPEND t GPr)`)]
AND_INTRO_THM)) THEN
UNDISCH_TAC (`((p:'a->bool) UNLESS q)(APPEND t GPr) /\
(p EXIST_TRANSITION q)(APPEND t GPr)`) THEN
REWRITE_TAC [SPECL [(`q:'a->bool`); (`p:'a->bool`);
(`APPEND (t:('a->'a)list) GPr`)]
(GEN_ALL (SYM (SPEC_ALL ENSURES)))] THEN
DISCH_TAC THEN
RES_TAC THENL
[
UNDISCH_TAC (`((p:'a->bool) ENSURES q) t`) THEN
REWRITE_TAC [ENSURES] THEN
STRIP_TAC THEN
ASM_REWRITE_TAC []
;
UNDISCH_TAC (`((p:'a->bool) ENSURES q) GPr`) THEN
REWRITE_TAC [ENSURES] THEN
STRIP_TAC THEN
ASM_REWRITE_TAC []
]]]);;
(*
Prove:
!p q FPr GPr.
(p ENSURES q) FPr /\ (p UNLESS q) GPr \/
(p ENSURES q) GPr /\ (p UNLESS q) FPr ==> (p ENSURES q) (APPEND FPr GPr)
*)
let COMP_ENSURES_thm1_lemma_2 = TAC_PROOF
(([],
`!(p:'a->bool) q FPr GPr.
((p ENSURES q) FPr /\ (p UNLESS q) GPr \/
(p ENSURES q) GPr /\ (p UNLESS q) FPr)
==> (p ENSURES q) (APPEND FPr GPr)`),
GEN_TAC THEN GEN_TAC THEN
LIST_INDUCT_TAC THEN
REWRITE_TAC [ENSURES;EXIST_TRANSITION;UNLESS;APPEND] THEN
REPEAT STRIP_TAC THEN
RES_TAC THEN
ASM_REWRITE_TAC [COMP_UNLESS_thm1;ENSURES;EXIST_TRANSITION;
UNLESS;APPEND] THEN
REWRITE_TAC [UNDISCH_ALL (ONCE_REWRITE_RULE [EXIST_TRANSITION_thm12]
(SPEC_ALL EXIST_TRANSITION_thm8))] THENL
[
REWRITE_TAC
[ONCE_REWRITE_RULE [EXIST_TRANSITION_thm12] (UNDISCH_ALL (SPECL
[`p:'a->bool`;`q:'a->bool`;`t:('a->'a)list`;`GPr:('a->'a)list`]
EXIST_TRANSITION_thm8))]
;
REWRITE_TAC
[UNDISCH_ALL
(SPECL [`p:'a->bool`;`q:'a->bool`;`GPr:('a->'a)list`;`t:('a->'a)list`]
EXIST_TRANSITION_thm8)]
]);;
(*
Prove:
!p q FPr GPr.
(p ENSURES q) (APPEND FPr GPr) = (p ENSURES q) FPr /\ (p UNLESS q) GPr \/
(p ENSURES q) GPr /\ (p UNLESS q) FPr
*)
let COMP_ENSURES_thm1 = prove_thm
("COMP_ENSURES_thm1",
(`!(p:'a->bool) q FPr GPr.
(p ENSURES q) (APPEND FPr GPr) <=>
((p ENSURES q) FPr /\ (p UNLESS q) GPr \/
(p ENSURES q) GPr /\ (p UNLESS q) FPr)`),
REPEAT GEN_TAC THEN
STRIP_ASSUME_TAC (IMP_ANTISYM_RULE
(SPEC_ALL COMP_ENSURES_thm1_lemma_1)
(SPEC_ALL COMP_ENSURES_thm1_lemma_2)));;
(*
Prove:
|- !p q FPr GPr.
(p ENSURES q)FPr /\ (p UNLESS q)GPr ==> (p ENSURES q)(APPEND FPr GPr)
*)
let COMP_ENSURES_cor0 = prove_thm
("COMP_ENSURES_cor0",
(`!(p:'a->bool) q FPr GPr.
(p ENSURES q) FPr /\ (p UNLESS q) GPr
==> (p ENSURES q) (APPEND FPr GPr)`),
REPEAT STRIP_TAC THEN
ACCEPT_TAC (REWRITE_RULE
[ASSUME (`((p:'a->bool) ENSURES q)FPr`);ASSUME (`((p:'a->bool) UNLESS q)GPr`)]
(SPEC_ALL COMP_ENSURES_thm1)));;
(*
Prove:
|- !p q FPr GPr.
(p ENSURES q)GPr /\ (p UNLESS q)FPr ==> (p ENSURES q)(APPEND FPr GPr)
*)
let COMP_ENSURES_cor1 = prove_thm
("COMP_ENSURES_cor1",
(`!(p:'a->bool) q FPr GPr.
(p ENSURES q) GPr /\ (p UNLESS q) FPr
==> (p ENSURES q) (APPEND FPr GPr)`),
REPEAT STRIP_TAC THEN
ACCEPT_TAC (REWRITE_RULE
[ASSUME (`((p:'a->bool) ENSURES q)GPr`);ASSUME (`((p:'a->bool) UNLESS q)FPr`)]
(SPEC_ALL COMP_ENSURES_thm1)));;
(*
Prove:
!p q FPr GPr.
(p INVARIANT q) (APPEND FPr GPr) =
(p INVARIANT q) FPr /\ (p INVARIANT q) GPr
*)
let COMP_UNITY_cor0 = prove_thm
("COMP_UNITY_cor0",
(`!(p0:'a->bool) p FPr GPr.
(p INVARIANT (p0, APPEND FPr GPr)) =
(p INVARIANT (p0,FPr) /\ p INVARIANT (p0,GPr))`),
REWRITE_TAC [INVARIANT;STABLE;COMP_UNLESS_thm1] THEN
REPEAT GEN_TAC THEN EQ_TAC THEN REPEAT STRIP_TAC THEN
RES_TAC THEN ASM_REWRITE_TAC []);;
(*
Prove:
!p FPr GPr.
p STABLE (APPEND FPr GPr) = p STABLE FPr /\ p STABLE GPr
*)
let COMP_UNITY_cor1 = prove_thm
("COMP_UNITY_cor1",
(`!(p:'a->bool) FPr GPr.
(p STABLE (APPEND FPr GPr)) = (p STABLE FPr /\ p STABLE GPr)`),
REWRITE_TAC [STABLE;COMP_UNLESS_thm1]);;
(*
Prove:
!p q FPr GPr.
(p UNLESS q) FPr /\ p STABLE GPr ==>(p UNLESS q) (APPEND FPr GPr)
*)
let COMP_UNITY_cor2 = prove_thm
("COMP_UNITY_cor2",
(`!(p:'a->bool) q FPr GPr.
(p UNLESS q) FPr /\ p STABLE GPr ==>(p UNLESS q) (APPEND FPr GPr)`),
REWRITE_TAC [STABLE;COMP_UNLESS_thm1] THEN
REPEAT STRIP_TAC THENL
[
ASM_REWRITE_TAC []
;
UNDISCH_TAC (`((p:'a->bool) UNLESS False)GPr`) THEN
SPEC_TAC ((`GPr:('a->'a)list`),(`GPr:('a->'a)list`)) THEN
LIST_INDUCT_TAC THENL
[
REWRITE_TAC [UNLESS]
;
REWRITE_TAC [UNLESS;UNLESS_STMT] THEN
CONV_TAC (DEPTH_CONV BETA_CONV) THEN
REPEAT STRIP_TAC THENL
[
RES_TAC THEN
UNDISCH_TAC
(`~(False:'a->bool) s ==> (p:'a->bool)(h s) \/ False(h s)`) THEN
REWRITE_TAC [FALSE_def;NOT_CLAUSES;OR_INTRO_THM1]
;
RES_TAC]]]);;
(*
Prove:
!p0 p FPr GPr.
p INVARIANT (p0; FPr) /\ p STABLE GPr
==> p INVARIANT (p0; (APPEND FPr GPr))
*)
let COMP_UNITY_cor3 = prove_thm
("COMP_UNITY_cor3",
(`!(p0:'a->bool) p FPr GPr.
p INVARIANT (p0, FPr) /\ p STABLE GPr ==>
p INVARIANT (p0, (APPEND FPr GPr))`),
REWRITE_TAC [INVARIANT;STABLE;COMP_UNLESS_thm1] THEN
REPEAT STRIP_TAC THENL
[
RES_TAC
;
ASM_REWRITE_TAC []
;
ASM_REWRITE_TAC []]);;
(*
Prove:
!p q FPr GPr.
(p ENSURES q) FPr /\ p STABLE GPr ==> (p ENSURES q) (APPEND FPr GPr)
*)
let COMP_UNITY_cor4 = prove_thm
("COMP_UNITY_cor4",
(`!(p:'a->bool) q FPr GPr.
(p ENSURES q) FPr /\ p STABLE GPr ==> (p ENSURES q) (APPEND FPr GPr)`),
REPEAT STRIP_TAC THEN
ASSUME_TAC (UNDISCH_ALL (SPECL
[(`p:'a->bool`);(`q:'a->bool`);(`FPr:('a->'a)list`)] ENSURES_cor2)) THEN
ASSUME_TAC (UNDISCH_ALL (SPECL
[(`((p:'a->bool) UNLESS q)FPr`);(`(p:'a->bool) STABLE GPr`)]
AND_INTRO_THM)) THEN
ASSUME_TAC (UNDISCH_ALL (SPECL
[(`p:'a->bool`);(`q:'a->bool`);(`FPr:('a->'a)list`);(`GPr:('a->'a)list`)]
COMP_UNITY_cor2)) THEN
REWRITE_TAC [ENSURES] THEN
ASM_REWRITE_TAC [] THEN
UNDISCH_TAC (`((p:'a->bool) ENSURES q)FPr`) THEN
REWRITE_TAC [ENSURES] THEN
STRIP_TAC THEN
UNDISCH_TAC (`((p:'a->bool) EXIST_TRANSITION q)FPr`) THEN
SPEC_TAC ((`FPr:('a->'a)list`),(`FPr:('a->'a)list`)) THEN
LIST_INDUCT_TAC THENL
[
REWRITE_TAC [EXIST_TRANSITION]
;
REWRITE_TAC [APPEND;EXIST_TRANSITION] THEN
REPEAT STRIP_TAC THENL
[
ASM_REWRITE_TAC []
;
RES_TAC THEN
ASM_REWRITE_TAC []]]);;
(*
Prove:
!p q FPr GPr. (p UNLESS q)(APPEND FPr GPr) ==> (p UNLESS q) GPr
*)
let COMP_UNITY_cor5 = prove_thm
("COMP_UNITY_cor5",
(`!(p:'a->bool) q FPr GPr. (p UNLESS q)(APPEND FPr GPr) ==> (p UNLESS q) GPr`),
REWRITE_TAC [COMP_UNLESS_thm1] THEN
REPEAT STRIP_TAC);;
(*
Prove:
!p q FPr GPr. (p UNLESS q)(APPEND FPr GPr) ==> (p UNLESS q) FPr
*)
let COMP_UNITY_cor6 = prove_thm
("COMP_UNITY_cor6",
(`!(p:'a->bool) q FPr GPr. (p UNLESS q)(APPEND FPr GPr) ==> (p UNLESS q) FPr`),
REWRITE_TAC [COMP_UNLESS_thm1] THEN
REPEAT STRIP_TAC);;
(*
Prove:
!p q st FPr. (p UNLESS q)(CONS st FPr) ==> (p UNLESS q) FPr
*)
let COMP_UNITY_cor7 = prove_thm
("COMP_UNITY_cor7",
(`!(p:'a->bool) q st FPr. (p UNLESS q)(CONS st FPr) ==> (p UNLESS q) FPr`),
REWRITE_TAC [UNLESS] THEN
REPEAT STRIP_TAC);;
(*
Prove:
!p FPr GPr.
(p ENSURES (NotX p)) FPr ==> (p ENSURES (NotX p)) (APPEND FPr GPr)
*)
let COMP_UNITY_cor8 = prove_thm
("COMP_UNITY_cor8",
(`!(p:'a->bool) FPr GPr.
(p ENSURES (Not p)) FPr ==> (p ENSURES (Not p)) (APPEND FPr GPr)`),
GEN_TAC THEN
LIST_INDUCT_TAC THEN
REWRITE_TAC [APPEND;ENSURES;UNLESS;EXIST_TRANSITION] THEN
REPEAT STRIP_TAC THEN
RES_TAC THEN
ASM_REWRITE_TAC [UNLESS_thm2] THEN
REWRITE_TAC [UNDISCH_ALL (ONCE_REWRITE_RULE [EXIST_TRANSITION_thm12] (SPECL
[`p:'a->bool`;`Not (p:'a->bool)`;`t:('a->'a)list`;`GPr:('a->'a)list`]
EXIST_TRANSITION_thm8))]);;
(*
Prove:
!p q FPr GPr.
p STABLE FPr /\ (p UNLESS q) GPr ==> (p UNLESS q) (APPEND FPr GPr)
*)
let COMP_UNITY_cor9 = prove_thm
("COMP_UNITY_cor9",
(`!(p:'a->bool) q FPr GPr.
p STABLE FPr /\ (p UNLESS q) GPr ==> (p UNLESS q) (APPEND FPr GPr)`),
REWRITE_TAC [STABLE;COMP_UNLESS_thm1] THEN
REPEAT STRIP_TAC THENL
[
UNDISCH_TAC (`((p:'a->bool) UNLESS False)FPr`) THEN
SPEC_TAC ((`FPr:('a->'a)list`),(`FPr:('a->'a)list`)) THEN
LIST_INDUCT_TAC THENL
[
REWRITE_TAC [UNLESS]
;
REWRITE_TAC [UNLESS;UNLESS_STMT] THEN
BETA_TAC THEN
REPEAT STRIP_TAC THENL
[
RES_TAC THEN
UNDISCH_TAC
(`~(False:'a->bool) s ==> (p:'a->bool)(h s) \/ False(h s)`) THEN
REWRITE_TAC [FALSE_def;NOT_CLAUSES;OR_INTRO_THM1]
;
RES_TAC
]
]
;
ASM_REWRITE_TAC []
]);;
(*
Prove:
!p q FPr GPr.
(p UNLESS q) (APPEND FPr GPr) = (p UNLESS q) (APPEND GPr FPr)
*)
let COMP_UNITY_cor10 = prove_thm
("COMP_UNITY_cor10",
(`!(p:'a->bool) q FPr GPr.
(p UNLESS q) (APPEND FPr GPr) = (p UNLESS q) (APPEND GPr FPr)`),
REPEAT GEN_TAC THEN
REWRITE_TAC [COMP_UNLESS_thm1] THEN
EQ_TAC THEN
REPEAT STRIP_TAC THEN
ASM_REWRITE_TAC []);;
(*
Prove:
!p q FPr GPr.
(p ENSURES q) (APPEND FPr GPr) = (p ENSURES q) (APPEND GPr FPr)
*)
let COMP_UNITY_cor11 = prove_thm
("COMP_UNITY_cor11",
(`!(p:'a->bool) q FPr GPr.
(p ENSURES q) (APPEND FPr GPr) = (p ENSURES q) (APPEND GPr FPr)`),
REPEAT GEN_TAC THEN
REWRITE_TAC [COMP_ENSURES_thm1] THEN
EQ_TAC THEN REPEAT STRIP_TAC THEN ASM_REWRITE_TAC []);;
(*
Prove:
!p q FPr GPr.
(p LEADSTO q) (APPEND FPr GPr) = (p LEADSTO q) (APPEND GPr FPr)
*)
(*
|- (!p' q'.
((p' ENSURES q')(APPEND Pr1 Pr2) ==> (p' LEADSTO q')(APPEND Pr2 Pr1)) /\
(!r.
(p' LEADSTO r)(APPEND Pr1 Pr2) /\ (p' LEADSTO r)(APPEND Pr2 Pr1) /\
(r LEADSTO q')(APPEND Pr1 Pr2) /\ (r LEADSTO q')(APPEND Pr2 Pr1) ==>
(p' LEADSTO q')(APPEND Pr1 Pr2) ==> (p' LEADSTO q')(APPEND Pr2 Pr1)) /\
(!P.
(!i. ((P i) LEADSTO q')(APPEND Pr1 Pr2)) /\
(!i. ((P i) LEADSTO q')(APPEND Pr2 Pr1)) ==>
(($ExistsX P) LEADSTO q')(APPEND Pr1 Pr2) ==>
(($ExistsX P) LEADSTO q')(APPEND Pr2 Pr1)))
==>
(p LEADSTO q)(APPEND Pr1 Pr2) ==> (p LEADSTO q)(APPEND Pr2 Pr1)
*)
let COMP_UNITY_cor12_lemma00 = (BETA_RULE (SPECL
[(`\(p:'a->bool) q. (p LEADSTO q)(APPEND Pr2 Pr1)`);
(`p:'a->bool`);(`q:'a->bool`);(`APPEND (Pr1:('a->'a)list) Pr2`)] LEADSTO_thm37));;
let COMP_UNITY_cor12_lemma01 = TAC_PROOF
(([],
(`!(p':'a->bool) q' Pr1 Pr2.
(p' ENSURES q')(APPEND Pr1 Pr2) ==> (p' LEADSTO q')(APPEND Pr2 Pr1)`)),
REPEAT STRIP_TAC THEN
ASSUME_TAC (ONCE_REWRITE_RULE [COMP_UNITY_cor11] (ASSUME
(`((p':'a->bool) ENSURES q')(APPEND Pr1 Pr2)`))) THEN
IMP_RES_TAC LEADSTO_thm0);;
let COMP_UNITY_cor12_lemma02 = TAC_PROOF
(([],
(`!(p':'a->bool) q' Pr1 Pr2.
(!r.
(p' LEADSTO r)(APPEND Pr1 Pr2) /\ (p' LEADSTO r)(APPEND Pr2 Pr1) /\
(r LEADSTO q')(APPEND Pr1 Pr2) /\ (r LEADSTO q')(APPEND Pr2 Pr1)
==> (p' LEADSTO q')(APPEND Pr2 Pr1))`)),
REPEAT STRIP_TAC THEN
IMP_RES_TAC LEADSTO_thm1);;
let COMP_UNITY_cor12_lemma03 = TAC_PROOF
(([],
(`!(p':'a->bool) q' Pr1 Pr2.
(!P:('a->bool)->bool.
(!p''. p'' In P ==> (p'' LEADSTO q')(APPEND Pr1 Pr2)) /\
(!p''. p'' In P ==> (p'' LEADSTO q')(APPEND Pr2 Pr1))
==> ((LUB P) LEADSTO q')(APPEND Pr2 Pr1))`)),
REPEAT STRIP_TAC THEN
IMP_RES_TAC LEADSTO_thm3a);;
(*
|- !p q Pr1 Pr2.
(p LEADSTO q)(APPEND Pr1 Pr2) ==> (p LEADSTO q)(APPEND Pr2 Pr1)
*)
let COMP_UNITY_cor12_lemma04 = (GEN_ALL (REWRITE_RULE
[COMP_UNITY_cor12_lemma01;COMP_UNITY_cor12_lemma02;COMP_UNITY_cor12_lemma03]
(SPEC_ALL COMP_UNITY_cor12_lemma00)));;
(*
|- !p q Pr1 Pr2. (p LEADSTO q)(APPEND Pr1 Pr2) = (p LEADSTO q)(APPEND Pr2 Pr1)
*)
let COMP_UNITY_cor12 = prove_thm
("COMP_UNITY_cor12",
(`!(p:'a->bool) q Pr1 Pr2.
(p LEADSTO q)(APPEND Pr1 Pr2) = (p LEADSTO q)(APPEND Pr2 Pr1)`),
REPEAT GEN_TAC THEN
EQ_TAC THEN REWRITE_TAC [COMP_UNITY_cor12_lemma04]);;
(*
|- !p FPr GPr. p STABLE (APPEND FPr GPr) = p STABLE (APPEND GPr FPr)
*)
let COMP_UNITY_cor13 = prove_thm
("COMP_UNITY_cor13",
(`!(p:'a->bool) FPr GPr.
(p STABLE (APPEND FPr GPr)) = (p STABLE (APPEND GPr FPr))`),
REPEAT GEN_TAC THEN
REWRITE_TAC [STABLE] THEN
EQ_TAC THEN
STRIP_TAC THEN
ONCE_REWRITE_TAC [COMP_UNITY_cor10] THEN
ASM_REWRITE_TAC []);;
(*
|- !p0 p FPr GPr.
p INVARIANT (p0, APPEND FPr GPr) = p INVARIANT (p0, APPEND GPr FPr)
*)
let COMP_UNITY_cor14 = prove_thm
("COMP_UNITY_cor14",
(`!(p0:'a->bool) p FPr GPr.
(p INVARIANT (p0, (APPEND FPr GPr)))
=
(p INVARIANT (p0, (APPEND GPr FPr)))`),
REPEAT GEN_TAC THEN
REWRITE_TAC [INVARIANT] THEN
EQ_TAC THEN
STRIP_TAC THEN
ONCE_REWRITE_TAC [COMP_UNITY_cor13] THEN
ASM_REWRITE_TAC []);;
|
