:: SCMFSA6C semantic presentation
set SA0 = Start-At (insloc 0);
theorem Th1: :: SCMFSA6C:1
theorem Th2: :: SCMFSA6C:2
:: deftheorem Def1 defines parahalting SCMFSA6C:def 1 :
:: deftheorem Def2 defines keeping_0 SCMFSA6C:def 2 :
Lemma42:
Macro (halt SCM+FSA ) is parahalting
Lemma56:
( Macro (halt SCM+FSA ) is keeping_0 & Macro (halt SCM+FSA ) is parahalting )
registration
let a be
Int-Location ,
b be
Int-Location ;
cluster a1 := a2 -> parahalting ;
coherence
a := b is parahalting
cluster AddTo a1,
a2 -> parahalting ;
coherence
AddTo a,b is parahalting
cluster SubFrom a1,
a2 -> parahalting ;
coherence
SubFrom a,b is parahalting
cluster MultBy a1,
a2 -> parahalting ;
coherence
MultBy a,b is parahalting
cluster Divide a1,
a2 -> parahalting ;
coherence
Divide a,b is parahalting
let f be
FinSeq-Location ;
cluster a2 := a3,
a1 -> parahalting ;
coherence
b := f,a is parahalting
cluster a3,
a1 := a2 -> parahalting keeping_0 ;
coherence
( f,a := b is parahalting & f,a := b is keeping_0 )
end;
:: deftheorem Def3 defines Initialize SCMFSA6C:def 3 :
theorem Th3: :: SCMFSA6C:3
theorem Th4: :: SCMFSA6C:4
theorem Th5: :: SCMFSA6C:5
E215:
now
let I be
parahalting keeping_0 Macro-Instruction;
let s be
State of
SCM+FSA ;
set IE =
IExec I,
s;
set IF =
Int-Locations \/ FinSeq-Locations ;
now
E39:
(
dom (Initialize (IExec I,s)) = the
carrier of
SCM+FSA &
dom (IExec I,s) = the
carrier of
SCM+FSA )
by AMI_3:36;
hence E45:
dom ((Initialize (IExec I,s)) | (Int-Locations \/ FinSeq-Locations )) = (dom (IExec I,s)) /\ (Int-Locations \/ FinSeq-Locations )
by RELAT_1:90;
let x be
set ;
assume E46:
x in dom ((Initialize (IExec I,s)) | (Int-Locations \/ FinSeq-Locations ))
;
dom (Initialize (IExec I,s)) = (Int-Locations \/ FinSeq-Locations ) \/ ({(IC SCM+FSA )} \/ the Instruction-Locations of SCM+FSA )
by , SCMFSA_2:8, XBOOLE_1:4;
then E47:
dom ((Initialize (IExec I,s)) | (Int-Locations \/ FinSeq-Locations )) = Int-Locations \/ FinSeq-Locations
by , , XBOOLE_1:21;
end;
hence
(Initialize (IExec I,s)) | (Int-Locations \/ FinSeq-Locations ) = (IExec I,s) | (Int-Locations \/ FinSeq-Locations )
by FUNCT_1:68;
end;
theorem Th6: :: SCMFSA6C:6
theorem Th7: :: SCMFSA6C:7
theorem Th8: :: SCMFSA6C:8
theorem Th9: :: SCMFSA6C:9
theorem Th10: :: SCMFSA6C:10
:: deftheorem Def4 defines swap SCMFSA6C:def 4 :
theorem Th11: :: SCMFSA6C:11
theorem Th12: :: SCMFSA6C:12