reserve a, b, d1, d2, d3, d4 for Int-Location,
  A, B for Data-Location,
  f, f1, f2, f3 for FinSeq-Location,
  il, i1, i2 for Nat,
  L for Nat,
  I for Instruction of SCM+FSA,
  s,s1,s2 for State of SCM+FSA,
  T for InsType of the InstructionsF of SCM+FSA,
  k for Nat;
reserve J,K for Element of Segm 13,
  b,b1,c,c1 for Element of SCM-Data-Loc,
  f,f1 for Element of SCM+FSA-Data*-Loc;
reserve a, b, d1, d2, d3, d4 for Int-Location,
  A, B for Data-Location,
  f, f1,
  f2, f3 for FinSeq-Location;

theorem Th24:
  T = 7 implies dom product" JumpParts T = {1}
proof
  set i1 = the Nat,a = the Int-Location;
  assume
A1: T = 7;
A2: JumpPart (a =0_goto i1) = <*i1*> by Th15;
  hereby
    let x be object;
    InsCode (a =0_goto i1) = 7 by SCMFSA_2:24;
    then
A3: 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 A3,CARD_3:108;
    hence x in {1} by A2,FINSEQ_1:2,38;
  end;
  let x be object;
  assume
A4: 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+FSA such that
A5: f = JumpPart I and
A6: InsCode I = T;
    consider i1, a such that
A7: I = a =0_goto i1 by A1,A6,SCMFSA_2:36;
    f = <*i1*> by A5,A7,Th15;
    hence thesis by A4,FINSEQ_1:2,38;
  end;
   then x in DOM JumpParts T by CARD_3:109;
  hence thesis by CARD_3:def 12;
end;
