reserve x for set,
  k for Element of NAT;
reserve s for State of SCMPDS;
reserve d1,d2,d3,d4,d5 for Element of SCM-Data-Loc,
  k1,k2,k3,k4,k5,k6 for Integer;
reserve I for Instruction of SCMPDS;
reserve a,b,c for Int_position;

theorem Th51:
  Exec(goto k1, s).IC SCMPDS = ICplusConst(s,k1) & for a holds
  Exec(goto k1, s).a = s.a
proof
  reconsider i = 14 as Element of Segm 15 by NAT_1:44;
  reconsider I = goto k1 as Element of SCMPDS-Instr;
  reconsider S = s as SCM-State by CARD_3:107;
 I = [ i,{}, <*k1*>];
  then
A1: I const_INT = k1 by SCMPDS_I:4;
A2: InsCode(I) = 14;
A3: Exec(goto k1, s) = SCM-Exec-Res(I,S) by SCMPDS_1:def 23
    .=SCM-Chg(S,jump_address(S,I const_INT)) by A2,SCMPDS_1:def 22;
  ex n be Element of NAT st n=IC s & ICplusConst(s,k1)=|.n+k1.| by Def17;
  hence Exec(goto k1, s).IC SCMPDS =ICplusConst(s,k1) by A3,A1,Th1,AMI_2:11;
  let a;
  reconsider mn = a as Element of SCM-Data-Loc by AMI_2:def 16;
  thus Exec(goto k1, s).a = S.mn by A3,AMI_2:12
    .= s.a;
end;
