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 = 5 implies JumpParts T = {{}}
proof
  assume
A1: T = 5;
  hereby
    let x be object;
    assume x in JumpParts T;
     then consider I being Instruction of SCM R such that
A2:   x = JumpPart I and
A3:   InsCode I = T;
     consider a,r such that
A4:   I = a:=r by A1,A3,Th16;
     x = {} by A2,A4;
    hence x in {{}} by TARSKI:def 1;
  end;
  set a = the Data-Location of R, r = the Element of R;
  let x be object;
  assume x in {{}};
   then x = {} by TARSKI:def 1;
   then
A5:  x = JumpPart(a:=r);
    InsCode(a:=r) = 5;
  hence thesis by A5,A1;
end;
