reserve I for Element of Segm 8,
  S for non empty 1-sorted,
  t for Element of S,
  x for set,
  k for Element of NAT;
 reserve R for Ring, T for InsType of SCM-Instr R;
reserve R for Ring,
  r for Element of R,
  a, b, c, d1, d2 for Data-Location of R,
  i1 for Nat;
reserve s for State of SCM R;

theorem
  Exec(goto(i1,R), s).IC SCM R = i1 & Exec(goto(i1,R), s).c = s.c
proof
A1: the_Values_of SCM R = (SCM-VAL R)*SCM-OK by Lm1;
  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 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,I jump_address)) by SCMRING1:def 14,A3;
  thus Exec(goto(i1,R), s).IC SCM R = Exec(goto(i1,R), s).NAT by Def1
    .= i1 by A4,A2,SCMRING1:7;
  c is Element of Data-Locations SCM by Th1;
  hence thesis by A4,AMI_3:27,SCMRING1:8;
end;
