reserve x,A for set,
  i,j,k,m,n, l, l1, l2 for Nat;
reserve D for non empty set,
  z for Nat;
reserve y for set;

theorem
 for S being homogeneous standard-ins non empty set
 for I being Element of S st JumpPart I = {}
  holds JumpParts InsCode I = {0}
proof let S be homogeneous standard-ins non empty set;
 let I be Element of S;
  assume
A1: JumpPart I = {};
   set T = InsCode I;
  hereby
    let a be object;
    assume a in JumpParts T;
    then consider II being Element of S such that
A2: a = JumpPart II and
A3: InsCode II = T;
    dom JumpPart II = dom JumpPart I by A3,Def5;
    then a = 0 by A1,A2;
   hence a in {0} by TARSKI:def 1;
  end;
  let a be object;
  assume a in {0};
  then a = 0 by TARSKI:def 1;
  hence a in JumpParts T by A1;
end;
