reserve a, b, d1, d2 for Data-Location,
  il, i1, i2 for Nat,
  I for Instruction of SCM,
  s, s1, s2 for State of SCM,
  T for InsType of the InstructionsF of SCM,
  k,k1 for Nat;

theorem Th10:
  T = 7 implies dom product" JumpParts T = {1}
proof
  set i1 = the Element of NAT,a = the Data-Location;
  assume
A1: T = 7;
  hereby
    let x be object;
    InsCode (a =0_goto i1) = 7;
    then
A2: JumpPart (a =0_goto i1) in JumpParts T by A1;
    assume x in dom product" JumpParts T;
    then x in DOM JumpParts T by CARD_3:def 12;
    then x in dom JumpPart (a =0_goto i1) by A2,CARD_3:108;
    hence x in {1} by FINSEQ_1:2,38;
  end;
  let x be object;
  assume
A3: x in {1};
  for f being Function st f in JumpParts T holds x in dom f
  proof
    let f be Function;
    assume f in JumpParts T;
    then consider I being Instruction of SCM such that
A4: f = JumpPart I and
A5: InsCode I = T;
    consider i1, a such that
A6: I = a =0_goto i1 by A1,A5,AMI_5:14;
    f = <*i1*> by A4,A6;
    hence thesis by A3,FINSEQ_1:2,38;
  end;
   then x in DOM JumpParts T by CARD_3:109;
  hence thesis by CARD_3:def 12;
end;
