let l be Element of NAT ; :: thesis: for s being State of SCM+FSA holds
( (Exec ((goto l),s)) . (IC SCM+FSA) = l & ( for c being Int-Location holds (Exec ((goto l),s)) . c = s . c ) & ( for f being FinSeq-Location holds (Exec ((goto l),s)) . f = s . f ) )
let s be State of SCM+FSA; :: thesis: ( (Exec ((goto l),s)) . (IC SCM+FSA) = l & ( for c being Int-Location holds (Exec ((goto l),s)) . c = s . c ) & ( for f being FinSeq-Location holds (Exec ((goto l),s)) . f = s . f ) )
consider La being Element of NAT such that
A1: l = La and
A2: goto l = SCM-goto La ;
reconsider S = (s | SCM-Memory) +* (NAT --> (SCM-goto La)) as State of SCM by Th73;
A3: Exec ((goto l),s) = (s +* (Exec ((SCM-goto La),S))) +* (s | NAT) by A2, Th75;
hence (Exec ((goto l),s)) . (IC SCM+FSA) = (Exec ((SCM-goto La),S)) . (IC SCM) by Th78
.= l by A1, AMI_3:13 ;
:: thesis: ( ( for c being Int-Location holds (Exec ((goto l),s)) . c = s . c ) & ( for f being FinSeq-Location holds (Exec ((goto l),s)) . f = s . f ) )

hereby :: thesis: for f being FinSeq-Location holds (Exec ((goto l),s)) . f = s . f

let c be Int-Location ; :: thesis: (Exec ((goto l),s)) . c = s . c
reconsider C = c as Data-Location by Th25;
thus (Exec ((goto l),s)) . c = (Exec ((SCM-goto La),S)) . C by A3, Th79
.= S . C by AMI_3:13
.= s . c by Th80 ; :: thesis: verum

end;

let f be FinSeq-Location ; :: thesis: (Exec ((goto l),s)) . f = s . f

A4: now

assume f in NAT ; :: thesis: contradiction
then A5: SCM+FSA-OK . f = SCM+FSA-Instr by SCMFSA_1:11;
f in SCM+FSA-Data*-Loc by Def5;
hence contradiction by A5, SCMFSA_1:12, SCMFSA_1:13; :: thesis: verum

end;

A6: not f in dom (Exec ((SCM-goto La),S)) by Th68;
dom (s | NAT) = (dom s) /\ NAT by RELAT_1:90;
then not f in dom (s | NAT) by A4, XBOOLE_0:def 4;
hence (Exec ((goto l),s)) . f = (s +* (Exec ((SCM-goto La),S))) . f by A3, FUNCT_4:12
.= s . f by A6, FUNCT_4:12 ;
:: thesis: verum