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

Step	Using
$((\forall X) \land (X \in integers) \land (\forall Y) \land (Y \in integers) \land ((X * Y) = 0) \Rightarrow ((X = 0) \lor (Y = 0)))$
$(((\forall X) \land (X \in integers) \land (\forall Y) \land (Y \in integers) \land \neg (((X * Y) = 0) \land (X \neq 0) \land (Y \neq 0))))$	Inversion
$(((\forall X) \land (X \in integers) \land (\forall Y) \land (Y \in integers) \land \neg (((X * Y) = 0) \land (X \neq 0) \land (Y \neq 0) \land ((X * 0) = 0))))$	Induction zero_times
$(((\forall X) \land (X \in integers) \land (\forall Y) \land (Y \in integers) \land \neg (((X * Y) = 0) \land (X \neq 0) \land (Y \neq 0) \land ((X * 0) = 0) \land ((X * Y) = (X * 0)))))$	Inference
$true$	Induction division