x : 0 ≤ x * x. Proof. apply not_lt_le_flip. intros E. destruct (lt_antisym (x * x) 0). split; [trivial |]. apply square_pos. pose proof pseudo_order_apart. apply (strong_extensionality (x *.)). rewrite mult_0_r. apply lt_apart. trivial. Qed.
Require Import