reserve i,j,k for Nat;
reserve I,J,K for Element of Segm 9,
  a,a1,a2 for Nat,
  b,b1,b2,c,c1 for Element of SCM-Data-Loc;
reserve T for InsType of SCM-Instr,
        I for Element of SCM-Instr;
reserve a,b,c for Data-Location,
  loc for Nat,
  I for Instruction of SCM;
reserve s for State of SCM;

theorem
  Exec(SCM-goto loc, s).IC SCM = loc & Exec(SCM-goto loc, s).c = s.c
proof
  reconsider mn = c as Element of SCM-Data-Loc by AMI_2:def 16;
  reconsider mj = loc as Element of NAT by ORDINAL1:def 12;
  reconsider I = SCM-goto loc as Element of SCM-Instr;
  reconsider S = s as SCM-State by CARD_3:107;
  reconsider i = 6 as Element of Segm 9 by NAT_1:44;
A1: I = [ i, <*mj*>, {} ];
A2: Exec(SCM-goto loc, s) = SCM-Exec-Res(I,S) by AMI_2:def 15
    .= (SCM-Chg(S,I jump_address)) by AMI_2:def 14;
  I jump_address = mj by A1,SCM_INST:6;
  hence Exec(SCM-goto loc, s).IC SCM = loc by A2,Th1,AMI_2:11;
  thus Exec(SCM-goto loc, s).c = S.mn by A2,AMI_2:12
    .= s.c;
end;
