set w = the State of SCM+FSA;
set t = the State of SCM+FSA +* (((intloc 0),(intloc 1)) --> (1,0));
A15: InsCode (MultBy (a,b)) =
4
by SCMFSA_2:21
.=
InsCode (MultBy ((intloc 0),(intloc 1)))
by SCMFSA_2:21
;
A16:
dom (((intloc 0),(intloc 1)) --> (1,0)) = {(intloc 0),(intloc 1)}
by FUNCT_4:62;
then
intloc 0 in dom (((intloc 0),(intloc 1)) --> (1,0))
by TARSKI:def 2;
then A17: ( the State of SCM+FSA +* (((intloc 0),(intloc 1)) --> (1,0))) . (intloc 0) =
(((intloc 0),(intloc 1)) --> (1,0)) . (intloc 0)
by FUNCT_4:13
.=
1
by AMI_3:10, FUNCT_4:63
;
intloc 0 in Int-Locations
by AMI_2:def 16;
then A18:
intloc 0 in Data-Locations
by SCMFSA_2:100, XBOOLE_0:def 3;
intloc 1 in dom (((intloc 0),(intloc 1)) --> (1,0))
by A16, TARSKI:def 2;
then A19: ( the State of SCM+FSA +* (((intloc 0),(intloc 1)) --> (1,0))) . (intloc 1) =
(((intloc 0),(intloc 1)) --> (1,0)) . (intloc 1)
by FUNCT_4:13
.=
0
by FUNCT_4:63
;
(Exec ((MultBy ((intloc 0),(intloc 1))),( the State of SCM+FSA +* (((intloc 0),(intloc 1)) --> (1,0))))) . (intloc 0) =
(( the State of SCM+FSA +* (((intloc 0),(intloc 1)) --> (1,0))) . (intloc 0)) * (( the State of SCM+FSA +* (((intloc 0),(intloc 1)) --> (1,0))) . (intloc 1))
by SCMFSA_2:66
.=
0
by A19
;
hence
for b1 being InsType of the InstructionsF of SCM+FSA st b1 = InsCode (MultBy (a,b)) holds
not b1 is jump-only
by A15, A17, A18; verum