let a, b be Int-Location; for s being State of SCM+FSA holds
( (Exec ((a := b),s)) . (IC ) = (IC s) + 1 & (Exec ((a := b),s)) . a = s . b & ( for c being Int-Location st c <> a holds
(Exec ((a := b),s)) . c = s . c ) & ( for f being FinSeq-Location holds (Exec ((a := b),s)) . f = s . f ) )
let s be State of SCM+FSA; ( (Exec ((a := b),s)) . (IC ) = (IC s) + 1 & (Exec ((a := b),s)) . a = s . b & ( for c being Int-Location st c <> a holds
(Exec ((a := b),s)) . c = s . c ) & ( for f being FinSeq-Location holds (Exec ((a := b),s)) . f = s . f ) )
consider A, B being Data-Location such that
A1:
a = A
and
A2:
b = B
and
A3:
a := b = A := B
by Def6;
reconsider S = s | SCM-Memory as State of SCM by Th42;
A4:
Exec ((a := b),s) = s +* (Exec ((A := B),S))
by A3, Th44;
hence (Exec ((a := b),s)) . (IC ) =
(Exec ((A := B),S)) . (IC )
by Th46
.=
(IC S) + 1
by AMI_3:2
.=
(IC s) + 1
by Th55
;
( (Exec ((a := b),s)) . a = s . b & ( for c being Int-Location st c <> a holds
(Exec ((a := b),s)) . c = s . c ) & ( for f being FinSeq-Location holds (Exec ((a := b),s)) . f = s . f ) )
thus (Exec ((a := b),s)) . a =
(Exec ((A := B),S)) . A
by A1, A4, Th47
.=
S . B
by AMI_3:2
.=
s . b
by A2, Th48
; ( ( for c being Int-Location st c <> a holds
(Exec ((a := b),s)) . c = s . c ) & ( for f being FinSeq-Location holds (Exec ((a := b),s)) . f = s . f ) )
let f be FinSeq-Location ; (Exec ((a := b),s)) . f = s . f
A6:
not f in dom (Exec ((A := B),S))
by Th37;
thus
(Exec ((a := b),s)) . f = s . f
by A4, A6, FUNCT_4:11; verum