(* Advanced properties ******************************************************)
-(* Basic_2A1: uses: lleq_refl *)
lemma lfdeq_refl: ∀h,o,T. reflexive … (lfdeq h o T).
/2 width=1 by lfxs_refl/ qed.
-lemma lfdeq_pair: ∀h,o,V1,V2. V1 ≡[h, o] V2 →
- ∀I,L. ∀T:term. L.ⓑ{I}V1 ≡[h, o, T] L.ⓑ{I}V2.
-/2 width=1 by lfxs_pair/ qed.
+lemma lfdeq_pair_refl: ∀h,o,V1,V2. V1 ≛[h, o] V2 →
+ ∀I,L. ∀T:term. L.ⓑ{I}V1 ≛[h, o, T] L.ⓑ{I}V2.
+/2 width=1 by lfxs_pair_refl/ qed.
(* Advanced inversion lemmas ************************************************)
-lemma lfdeq_inv_bind_void: â\88\80h,o,p,I,L1,L2,V,T. L1 â\89¡[h, o, ⓑ{p,I}V.T] L2 →
- L1 â\89¡[h, o, V] L2 â\88§ L1.â\93§ â\89¡[h, o, T] L2.ⓧ.
+lemma lfdeq_inv_bind_void: â\88\80h,o,p,I,L1,L2,V,T. L1 â\89\9b[h, o, ⓑ{p,I}V.T] L2 →
+ L1 â\89\9b[h, o, V] L2 â\88§ L1.â\93§ â\89\9b[h, o, T] L2.ⓧ.
/2 width=3 by lfxs_inv_bind_void/ qed-.
(* Advanced forward lemmas **************************************************)
lemma lfdeq_fwd_bind_dx_void: ∀h,o,p,I,L1,L2,V,T.
- L1 â\89¡[h, o, â\93\91{p,I}V.T] L2 â\86\92 L1.â\93§ â\89¡[h, o, T] L2.ⓧ.
+ L1 â\89\9b[h, o, â\93\91{p,I}V.T] L2 â\86\92 L1.â\93§ â\89\9b[h, o, T] L2.ⓧ.
/2 width=4 by lfxs_fwd_bind_dx_void/ qed-.