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, x being set st x in dom JumpPart I holds
  (JumpPart I).x in (product" JumpParts InsCode I).x
proof
  let S be homogeneous J/A-independent standard-ins non empty set,
  I be Element of S, x be set such that
A1: x in dom JumpPart I;
A2: JumpPart I in JumpParts InsCode I;
A3: dom product" JumpParts InsCode I = DOM JumpParts InsCode I
  by CARD_3:def 12
    .= dom JumpPart I by A2,CARD_3:108;
  (JumpPart I).x in pi(JumpParts InsCode I,x) by A2,CARD_3:def 6;
  hence thesis
  by A1,A3,CARD_3:def 12;
end;
