(* Basic_2A1: uses: lleq_inv_lift_le lleq_inv_lift_be lleq_inv_lift_ge *)
lemma lfdeq_inv_lifts_bi: ∀h,o,L1,L2,U. L1 ≛[h, o, U] L2 → ∀b,f. 𝐔⦃f⦄ →
- â\88\80K1,K2. â¬\87*[b, f] L1 â\89¡ K1 â\86\92 â¬\87*[b, f] L2 â\89¡ K2 →
- â\88\80T. â¬\86*[f] T â\89¡ U → K1 ≛[h, o, T] K2.
+ â\88\80K1,K2. â¬\87*[b, f] L1 â\89\98 K1 â\86\92 â¬\87*[b, f] L2 â\89\98 K2 →
+ â\88\80T. â¬\86*[f] T â\89\98 U → K1 ≛[h, o, T] K2.
/2 width=10 by lfxs_inv_lifts_bi/ qed-.
-lemma lfdeq_inv_lref_pair_sn: â\88\80h,o,L1,L2,i. L1 â\89\9b[h, o, #i] L2 â\86\92 â\88\80I,K1,V1. â¬\87*[i] L1 â\89¡ K1.ⓑ{I}V1 →
- â\88\83â\88\83K2,V2. â¬\87*[i] L2 â\89¡ K2.ⓑ{I}V2 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
+lemma lfdeq_inv_lref_pair_sn: â\88\80h,o,L1,L2,i. L1 â\89\9b[h, o, #i] L2 â\86\92 â\88\80I,K1,V1. â¬\87*[i] L1 â\89\98 K1.ⓑ{I}V1 →
+ â\88\83â\88\83K2,V2. â¬\87*[i] L2 â\89\98 K2.ⓑ{I}V2 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
/2 width=3 by lfxs_inv_lref_pair_sn/ qed-.
-lemma lfdeq_inv_lref_pair_dx: â\88\80h,o,L1,L2,i. L1 â\89\9b[h, o, #i] L2 â\86\92 â\88\80I,K2,V2. â¬\87*[i] L2 â\89¡ K2.ⓑ{I}V2 →
- â\88\83â\88\83K1,V1. â¬\87*[i] L1 â\89¡ K1.ⓑ{I}V1 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
+lemma lfdeq_inv_lref_pair_dx: â\88\80h,o,L1,L2,i. L1 â\89\9b[h, o, #i] L2 â\86\92 â\88\80I,K2,V2. â¬\87*[i] L2 â\89\98 K2.ⓑ{I}V2 →
+ â\88\83â\88\83K1,V1. â¬\87*[i] L1 â\89\98 K1.ⓑ{I}V1 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
/2 width=3 by lfxs_inv_lref_pair_dx/ qed-.