theorem
  (product" JumpParts InsCode (a >0_goto i1)).1 = NAT
proof
  dom product" JumpParts InsCode (a >0_goto i1) = {1} by Th25,SCMFSA_2:25;
  then
A1: 1 in dom product" JumpParts InsCode (a >0_goto i1) by TARSKI:def 1;
  hereby
    let x be object;
    assume x in (product" JumpParts InsCode (a >0_goto i1)).1;
    then x in pi(JumpParts InsCode (a >0_goto i1),1) by A1,CARD_3:def 12;
    then consider g being Function such that
A2: g in JumpParts InsCode (a >0_goto i1) and
A3: x = g.1 by CARD_3:def 6;
    consider I being Instruction of SCM+FSA such that
A4: g = JumpPart I and
A5: InsCode I = InsCode (a >0_goto i1) by A2;
    consider i2, b such that
A6: I = b >0_goto i2 by A5,SCMFSA_2:25,37;
    g = <*i2*> by A4,A6,Th16;
    then x = i2 by A3;
    hence x in NAT by ORDINAL1:def 12;
  end;
  let x be object;
  assume x in NAT;
  then reconsider x as Element of NAT;
A7: <*x*>.1 = x;
  InsCode (a >0_goto i1) = 8 by SCMFSA_2:25;
  then
A8: InsCode (a >0_goto i1) = InsCode (a >0_goto x) by SCMFSA_2:25;
  JumpPart (a >0_goto x) = <*x*> by Th16;
  then <*x*> in JumpParts InsCode (a >0_goto i1) by A8;
  then x in pi(JumpParts InsCode (a >0_goto i1),1) by A7,CARD_3:def 6;
  hence thesis by A1,CARD_3:def 12;
end;
