let s be State of SCMPDS ; :: thesis: for k1 being Integer
for a being Int_position holds
( (Exec (a := k1),s) . (IC SCMPDS ) = succ (IC s) & (Exec (a := k1),s) . a = k1 & ( for b being Int_position st b <> a holds
(Exec (a := k1),s) . b = s . b ) )
let k1 be Integer; :: thesis: for a being Int_position holds
( (Exec (a := k1),s) . (IC SCMPDS ) = succ (IC s) & (Exec (a := k1),s) . a = k1 & ( for b being Int_position st b <> a holds
(Exec (a := k1),s) . b = s . b ) )
let a be Int_position ; :: thesis: ( (Exec (a := k1),s) . (IC SCMPDS ) = succ (IC s) & (Exec (a := k1),s) . a = k1 & ( for b being Int_position st b <> a holds
(Exec (a := k1),s) . b = s . b ) )
reconsider S = s as SCMPDS-State by PBOOLE:155;
reconsider mk = a as Element of SCM-Data-Loc by Def2;
reconsider I = a := k1 as Element of SCMPDS-Instr ;
set S1 = SCM-Chg S,(I P21address ),(I P22const );
reconsider i = 2 as Element of Segm 14 by NAT_1:45;
A1: I = [i,{} ,<*mk,k1*>] ;
then A2: I P21address = mk by SCMPDS_1:35;
A3: I P22const = k1 by A1, SCMPDS_1:35;
A4: Exec (a := k1),s = SCM-Exec-Res I,S by SCMPDS_1:def 25
.= SCM-Chg (SCM-Chg S,(I P21address ),(I P22const )),(succ (IC S)) by A1, SCMPDS_1:def 24 ;
hence (Exec (a := k1),s) . (IC SCMPDS ) = succ (IC s) by Th6, SCMPDS_1:26; :: thesis: ( (Exec (a := k1),s) . a = k1 & ( for b being Int_position st b <> a holds
(Exec (a := k1),s) . b = s . b ) )
thus (Exec (a := k1),s) . a = (SCM-Chg S,(I P21address ),(I P22const )) . mk by A4, SCMPDS_1:27
.= k1 by A2, A3, SCMPDS_1:30 ; :: thesis: for b being Int_position st b <> a holds
(Exec (a := k1),s) . b = s . b
let b be Int_position ; :: thesis: ( b <> a implies (Exec (a := k1),s) . b = s . b )
reconsider mn = b as Element of SCM-Data-Loc by Def2;
assume A5: b <> a ; :: thesis: (Exec (a := k1),s) . b = s . b
thus (Exec (a := k1),s) . b = (SCM-Chg S,(I P21address ),(I P22const )) . mn by A4, SCMPDS_1:27
.= s . b by A2, A5, SCMPDS_1:31 ; :: thesis: verum