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
  T = 0 implies JumpParts T = {0}
proof
  assume
A1: T = 0;
  hereby
    let a be object;
    assume a in JumpParts T;
    then consider I such that
A2: a = JumpPart I and
A3: InsCode I = T;
    I = halt SCM R by A1,A3,Th11;
    then a = {} by A2;
    hence a in {0} by TARSKI:def 1;
  end;
  let a be object;
  assume a in {0};
  then
A4: a = 0 by TARSKI:def 1;
  InsCode halt SCM R = 0 & JumpPart halt SCM R = 0;
  hence thesis by A1,A4;
end;
