lemma reqx_inv_lifts_dx: f_dropable_dx cdeq.
/2 width=5 by rex_dropable_dx/ qed-.
-lemma reqx_inv_lifts_bi: â\88\80L1,L2,U. L1 â\89\9b[U] L2 â\86\92 â\88\80b,f. ð\9d\90\94â¦\83fâ¦\84 →
+lemma reqx_inv_lifts_bi: â\88\80L1,L2,U. L1 â\89\9b[U] L2 â\86\92 â\88\80b,f. ð\9d\90\94â\9dªfâ\9d« →
∀K1,K2. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 →
∀T. ⇧*[f] T ≘ U → K1 ≛[T] K2.
/2 width=10 by rex_inv_lifts_bi/ qed-.
-lemma reqx_inv_lref_pair_sn: ∀L1,L2,i. L1 ≛[#i] L2 → ∀I,K1,V1. ⇩*[i] L1 ≘ K1.ⓑ{I}V1 →
- ∃∃K2,V2. ⇩*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ≛[V1] K2 & V1 ≛ V2.
+lemma reqx_inv_lref_pair_sn: ∀L1,L2,i. L1 ≛[#i] L2 → ∀I,K1,V1. ⇩[i] L1 ≘ K1.ⓑ[I]V1 →
+ ∃∃K2,V2. ⇩[i] L2 ≘ K2.ⓑ[I]V2 & K1 ≛[V1] K2 & V1 ≛ V2.
/2 width=3 by rex_inv_lref_pair_sn/ qed-.
-lemma reqx_inv_lref_pair_dx: ∀L1,L2,i. L1 ≛[#i] L2 → ∀I,K2,V2. ⇩*[i] L2 ≘ K2.ⓑ{I}V2 →
- ∃∃K1,V1. ⇩*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ≛[V1] K2 & V1 ≛ V2.
+lemma reqx_inv_lref_pair_dx: ∀L1,L2,i. L1 ≛[#i] L2 → ∀I,K2,V2. ⇩[i] L2 ≘ K2.ⓑ[I]V2 →
+ ∃∃K1,V1. ⇩[i] L1 ≘ K1.ⓑ[I]V1 & K1 ≛[V1] K2 & V1 ≛ V2.
/2 width=3 by rex_inv_lref_pair_dx/ qed-.
lemma reqx_inv_lref_pair_bi (L1) (L2) (i):
L1 ≛[#i] L2 →
- ∀I1,K1,V1. ⇩*[i] L1 ≘ K1.ⓑ{I1}V1 →
- ∀I2,K2,V2. ⇩*[i] L2 ≘ K2.ⓑ{I2}V2 →
+ ∀I1,K1,V1. ⇩[i] L1 ≘ K1.ⓑ[I1]V1 →
+ ∀I2,K2,V2. ⇩[i] L2 ≘ K2.ⓑ[I2]V2 →
∧∧ K1 ≛[V1] K2 & V1 ≛ V2 & I1 = I2.
/2 width=6 by rex_inv_lref_pair_bi/ qed-.