proposition: Lemma ax_conv_con p q s : prv ([(p;;q)^^]s <--> [q^^;;p^^]s).
proof: Proof. rule axAI. - rewrite <- (ax_convEF (p;;q) s) at 2. rewrite -> ax_Con, ax_ConE. by do 2 rewrite <- ax_convBB. - rewrite -> ax_Con, (axConvF (p;;q)^^ [q^^][p^^]s), ax_conv,ax_Con; do ! restore. rewrite -> dmAX, dmAX, axDNE. by do 2 rewrite -> ax_convEF. Qed.
imports: Relations Lia Setoid Morphisms mathcomp(all_ssreflect) CompDecModal.libs(edone bcase fset base modular_hilbert sltype rewrite_inequality fset_tac)