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 ) = 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 ) = 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 ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )
let s be State of (SCM R); :: thesis: ( (Exec ((goto (i1,R)),s)) . (IC ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )
A1: the Object-Kind of (SCM R) = SCM-OK R by Def1;
reconsider S = s as SCM-State of R by A1, CARD_3:107;
reconsider i = 6 as Element of Segm 8 by NAT_1:44;
reconsider I = goto (i1,R) as Element of SCM-Instr R by Def1;
I = [i,<*i1*>,{}] ;
then A2: I jump_address = i1 by SCMRING1:14;
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 ) = (Exec ((goto (i1,R)),s)) . NAT by Def1
.= i1 by A3, A2, SCMRING1:7 ; :: thesis: (Exec ((goto (i1,R)),s)) . c = s . c
c is Element of Data-Locations by Th1;
hence (Exec ((goto (i1,R)),s)) . c = s . c by A3, AMI_3:27, SCMRING1:8; :: thesis: verum