reserve G for Abelian add-associative right_complementable right_zeroed
  non empty addLoopStr;
reserve GS for non empty addLoopStr;
reserve F for Field;
reserve F for Field,
  n for Nat,
  D for non empty set,
  d for Element of D,
  B for BinOp of D,
  C for UnOp of D;

theorem Th6:
  B is commutative implies product(B,n) is commutative
proof
  assume
A1: B is commutative;
  now
    let x,y be Element of n-tuples_on D;
    thus product(B,n).(x,y) = B.:(x,y) by Def1
      .= B.:(y,x) by A1,FINSEQOP:33
      .= product(B,n).(y,x) by Def1;
  end;
  hence thesis;
end;
