
theorem
  for A, Z be Element of Class EqBL2Nat,
  n be Nat,
  z be Element of BOOLEAN*
  st Z =Class (EqBL2Nat,z) & z =0*n
  holds A+Z = A & Z+A = A
  proof
    let A, Z be Element of Class EqBL2Nat,
    n be Nat,
    z be Element of BOOLEAN*;
    assume AS: Z =Class (EqBL2Nat,z) & z =0*n;
    reconsider zempty =<*> BOOLEAN as Element of BOOLEAN* by FINSEQ_1:def 11;
    Z =Class (EqBL2Nat,zempty) by AS,LM930;
    then
    P3: zempty in Z by EQREL_1:20;
    P4: len zempty = 0;
    P0: A in Class EqBL2Nat;
    consider x being object such that
    Q1: x in BOOLEAN* & A = Class (EqBL2Nat,x) by P0,EQREL_1:def 3;
    reconsider x as Element of BOOLEAN* by Q1;
    x in A by Q1,EQREL_1:20;
    hence A+Z = Class (EqBL2Nat,x+zempty) by P3,LM800
    .=A by Q1,P4,Def3;
    hence Z+A = A by LM910;
  end;
