let R be Ring; :: thesis: for c being Data-Location of R
for i1 being Nat
for s being State of (SCM R) holds
( (Exec ((goto (i1,R)),s)) . () = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

let c be Data-Location of R; :: thesis: for i1 being Nat
for s being State of (SCM R) holds
( (Exec ((goto (i1,R)),s)) . () = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

let i1 be Nat; :: thesis: for s being State of (SCM R) holds
( (Exec ((goto (i1,R)),s)) . () = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

let s be State of (SCM R); :: thesis: ( (Exec ((goto (i1,R)),s)) . () = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )
A1: the_Values_of (SCM R) = () * SCM-OK by Lm1;
reconsider S = s as SCM-State of R by ;
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 SCMRINGI:2;
A3: i1 in NAT by ORDINAL1:def 12;
A4: Exec ((goto (i1,R)),s) = SCM-Exec-Res (I,S) by Th10
.= SCM-Chg (S,()) by ;
thus (Exec ((goto (i1,R)),s)) . () = (Exec ((goto (i1,R)),s)) . NAT by Def1
.= i1 by ; :: 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 ; :: thesis: verum