If x * y = 0 then x or y is 0 proof

Step	Using
integer(X) and any(X) and integer(Y) and any(Y) and X * Y = 0=> X = 0 or Y = 0 ;
integer(X) and any(X) and integer(Y) and any(Y) and true=> not (X * Y = 0 and not X = 0 and not Y = 0) ;	Inversion
integer(X) and any(X) and integer(Y) and any(Y) and true=> not (X * Y = 0 and not X = 0 and not Y = 0 and X * 0 = 0) ;	Induction zero_times
integer(X) and any(X) and integer(Y) and any(Y) and true=> not (X * Y = 0 and not X = 0 and not Y = 0 and X * 0 = 0 and X * Y = X * 0) ;	Inference
true;	Induction division