let R be good Ring; :: thesis: for c being Data-Location of R
for i1 being Element of NAT
for s being State of (SCM R) holds
( (Exec (goto i1,R),s) . (IC (SCM R)) = i1 & (Exec (goto i1,R),s) . c = s . c )
let c be Data-Location of R; :: thesis: for i1 being Element of NAT
for s being State of (SCM R) holds
( (Exec (goto i1,R),s) . (IC (SCM R)) = i1 & (Exec (goto i1,R),s) . c = s . c )
let i1 be Element of NAT ; :: thesis: for s being State of (SCM R) holds
( (Exec (goto i1,R),s) . (IC (SCM R)) = i1 & (Exec (goto i1,R),s) . c = s . c )
let s be State of (SCM R); :: thesis: ( (Exec (goto i1,R),s) . (IC (SCM R)) = i1 & (Exec (goto i1,R),s) . c = s . c )
Y: the Object-Kind of (SCM R) = SCM-OK R by Def1;
reconsider S = s as SCM-State of R by Y, PBOOLE:155;
reconsider i = 6 as Element of Segm 8 by NAT_1:45;
reconsider I = goto i1,R as Element of SCM-Instr R by Def1;
I = [i,<*i1*>,{} ] ;
then A2: I jump_address = i1 by SCMRING1:18;
A3: Exec (goto i1,R),s = SCM-Exec-Res I,S by Th12
.= SCM-Chg S,(I jump_address ) by SCMRING1:def 14 ;
thus (Exec (goto i1,R),s) . (IC (SCM R)) = (Exec (goto i1,R),s) . NAT by Def1
.= i1 by A3, A2, SCMRING1:10 ; :: thesis: (Exec (goto i1,R),s) . c = s . c
c is Element of SCM-Data-Loc by Th1;
hence (Exec (goto i1,R),s) . c = s . c by A3, SCMRING1:11; :: thesis: verum