proposition: Lemma AbsCC_mult_conj : forall z : CC, z[*]CC_conj z [=] cc_IR (AbsCC z[^]2).
proof: Proof. intro z. unfold cc_IR in |- *. elim z. intros x y. apply eq_transitive_unfolded with (S := cc_csetoid) (y := cc_IR (x[^]2[+]y[^]2)). eapply l_1_1_2 with (x := x) (y := y). split; simpl in |- *. 2: algebra. eapply AbsCC_square_Re_Im with (x := x) (y := y). Qed.
imports: CoRN.complex.CComplex