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 J/A-independent standard-ins non empty set,
      I being Element of S
  holds JumpParts InsCode I = JumpParts InsCode IncAddr(I,k)
proof
  let S be homogeneous J/A-independent standard-ins non empty set,
      I be Element of S;
  set A = { JumpPart J where J is Element of S:
  InsCode I = InsCode J }, B = { JumpPart J where J is Element of S:
  InsCode IncAddr(I,k) = InsCode J };
  A = B
  proof
    hereby
      let a be object;
      assume a in A;
      then consider J being Element of S such that
A1:   a = JumpPart J and
A2:   InsCode J = InsCode I;
      InsCode J = InsCode IncAddr(I,k) by A2,Def8;
      hence a in B by A1;
    end;
    let a be object;
    assume a in B;
    then consider J being Element of S such that
A3: a = JumpPart J and
A4: InsCode J = InsCode IncAddr(I,k);
    InsCode J = InsCode I by A4,Def8;
    hence thesis by A3;
  end;
  hence thesis;
end;
