let s be State of SCMPDS; :: thesis: for k1 being Integer
for a being Int_position holds
( (Exec ((a := k1),s)) . (IC ) = 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 ) = 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 ) = 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 CARD_3:107;
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_1:44;
A1: I = [i,{},<*mk,k1*>] ;
then A2: I P21address = mk by SCMPDS_1:20;
A3: I P22const = k1 by A1, SCMPDS_1:20;
A4: Exec ((a := k1),s) = SCM-Exec-Res (I,S) by SCMPDS_1:def 23
.= SCM-Chg ((SCM-Chg (S,(I P21address),(I P22const))),(succ (IC S))) by A1, SCMPDS_1:def 22 ;
hence (Exec ((a := k1),s)) . (IC ) = succ (IC s) by Th6, SCMPDS_1:13; :: 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_1:14
.= k1 by A2, A3, SCMPDS_1:16 ; :: 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_1:14
.= s . b by A2, A5, SCMPDS_1:17 ; :: thesis: verum