/2 width=5 by rex_dropable_dx/ qed-.
lemma rdeq_inv_lifts_bi: ∀L1,L2,U. L1 ≛[U] L2 → ∀b,f. 𝐔⦃f⦄ →
- â\88\80K1,K2. â¬\87*[b,f] L1 â\89\98 K1 â\86\92 â¬\87*[b,f] L2 ≘ K2 →
- â\88\80T. â¬\86*[f] T ≘ U → K1 ≛[T] K2.
+ â\88\80K1,K2. â\87©*[b,f] L1 â\89\98 K1 â\86\92 â\87©*[b,f] L2 ≘ K2 →
+ â\88\80T. â\87§*[f] T ≘ U → K1 ≛[T] K2.
/2 width=10 by rex_inv_lifts_bi/ qed-.
-lemma rdeq_inv_lref_pair_sn: â\88\80L1,L2,i. L1 â\89\9b[#i] L2 â\86\92 â\88\80I,K1,V1. â¬\87*[i] L1 ≘ K1.ⓑ{I}V1 →
- â\88\83â\88\83K2,V2. â¬\87*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ≛[V1] K2 & V1 ≛ V2.
+lemma rdeq_inv_lref_pair_sn: â\88\80L1,L2,i. L1 â\89\9b[#i] L2 â\86\92 â\88\80I,K1,V1. â\87©*[i] L1 ≘ K1.ⓑ{I}V1 →
+ â\88\83â\88\83K2,V2. â\87©*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ≛[V1] K2 & V1 ≛ V2.
/2 width=3 by rex_inv_lref_pair_sn/ qed-.
-lemma rdeq_inv_lref_pair_dx: â\88\80L1,L2,i. L1 â\89\9b[#i] L2 â\86\92 â\88\80I,K2,V2. â¬\87*[i] L2 ≘ K2.ⓑ{I}V2 →
- â\88\83â\88\83K1,V1. â¬\87*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ≛[V1] K2 & V1 ≛ V2.
+lemma rdeq_inv_lref_pair_dx: â\88\80L1,L2,i. L1 â\89\9b[#i] L2 â\86\92 â\88\80I,K2,V2. â\87©*[i] L2 ≘ K2.ⓑ{I}V2 →
+ â\88\83â\88\83K1,V1. â\87©*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ≛[V1] K2 & V1 ≛ V2.
/2 width=3 by rex_inv_lref_pair_dx/ qed-.
lemma rdeq_inv_lref_pair_bi (L1) (L2) (i):
L1 ≛[#i] L2 →
- â\88\80I1,K1,V1. â¬\87*[i] L1 ≘ K1.ⓑ{I1}V1 →
- â\88\80I2,K2,V2. â¬\87*[i] L2 ≘ K2.ⓑ{I2}V2 →
+ â\88\80I1,K1,V1. â\87©*[i] L1 ≘ K1.ⓑ{I1}V1 →
+ â\88\80I2,K2,V2. â\87©*[i] L2 ≘ K2.ⓑ{I2}V2 →
∧∧ K1 ≛[V1] K2 & V1 ≛ V2 & I1 = I2.
/2 width=6 by rex_inv_lref_pair_bi/ qed-.