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

theorem Th25:
  T = 6 implies dom product" JumpParts T = {1}
proof
  set i1 = the Element of NAT;
  assume
A1: T = 6;
  hereby
    let x be object;
    InsCode goto(i1,R) = 6;
    then
A2: JumpPart goto(i1,R) 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 goto(i1,R) by A2,CARD_3:108;
    hence x in {1} by FINSEQ_1:2,def 8;
  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 R such that
A4: f = JumpPart I and
A5: InsCode I = T;
    consider i1 such that
A6: I = goto(i1,R) by A1,A5,Th17;
    f = <*i1*> by A4,A6;
    hence thesis by A3,FINSEQ_1:2,def 8;
  end;
   then x in DOM JumpParts T by CARD_3:109;
  hence thesis by CARD_3:def 12;
end;
