]
qed.
-lemma rex_unit_length (R): ∀L1,L2. |L1| = |L2| → ∀I. L1.ⓤ{I} ⪤[R,#0] L2.ⓤ{I}.
+lemma rex_unit_length (R): ∀L1,L2. |L1| = |L2| → ∀I. L1.ⓤ[I] ⪤[R,#0] L2.ⓤ[I].
/3 width=3 by rex_unit, sex_length_isid/ qed.
(* Basic_2A1: uses: llpx_sn_lift_le llpx_sn_lift_ge *)
∀Y1,Y2. Y1 ⪤[R,#0] Y2 →
∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
| ∃∃I,L1,L2,V1,V2. L1 ⪤[R,V1] L2 & R L1 V1 V2 &
- Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
- | ∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
+ Y1 = L1.ⓑ[I]V1 & Y2 = L2.ⓑ[I]V2
+ | ∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ[I] & Y2 = L2.ⓤ[I].
#R #Y1 #Y2 #H elim (rex_inv_zero … H) -H *
/4 width=9 by sex_fwd_length, ex4_5_intro, ex3_3_intro, or3_intro2, or3_intro1, or3_intro0, conj/
qed-.