reserve x for set,
  m,n for Nat,
  a,b,c for Int_position,
  i for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l1 for Nat,
  I,J for Program of SCMPDS,
  N for with_non-empty_elements set;
reserve P,P1,P2,Q for Instruction-Sequence of SCMPDS;

theorem Th10:
  InsCode i =1 implies i is not parahalting
proof
  consider s such that
A1: for a holds s.a = 2 by SCMPDS_2:61;
  set P = the Instruction-Sequence of SCMPDS;
  assume InsCode i=1;
  then consider a such that
A2: i = return a by SCMPDS_2:27;
  assume i is parahalting;
  then reconsider Li = Load i as parahalting Program of SCMPDS;
  set pi= Macro i;
  set s1=Initialize s, P1= P+*pi;
  s1.DataLoc(s1.a,RetIC)=s.DataLoc(s1.a,RetIC) by Th4
    .=2 by A1;
  then
A3: Exec(i, s1).IC SCMPDS =|.2.|+2 by A2,SCMPDS_2:58
    .= 2+2 by ABSVALUE:def 1
    .= 4;
  set C1=Comput(P1,s1,1);
   stop Li c= P1 by FUNCT_4:25;
   then
A4: IC C1 in dom pi by SCMPDS_4:def 6;
   0 in dom pi by COMPOS_1:57;
  then
A5: P1. 0= pi. 0 by FUNCT_4:13
    .=i by COMPOS_1:58;
A6: card pi = 2 by COMPOS_1:56;
A7: P1/.IC s1 = P1.IC s1 by PBOOLE:143;
  Comput(P1,s1,0+1) = Following(P1,Comput(P1,s1,0)) by EXTPRO_1:3
    .= Following(P1,s1)
    .= Exec(i, s1) by A5,A7,MEMSTR_0:47;
  hence contradiction by A3,A4,A6,AFINSQ_1:66;
end;
