qed-.
lemma tdeq_rex_div (R): ∀T1,T2. T1 ≛ T2 →
- ∀L1,L2. L1 ⪤[R, T2] L2 → L1 ⪤[R, T1] L2.
+ ∀L1,L2. L1 ⪤[R,T2] L2 → L1 ⪤[R,T1] L2.
/3 width=5 by tdeq_rex_conf, tdeq_sym/ qed-.
lemma tdeq_rdeq_conf: s_r_confluent1 … cdeq rdeq.
L1 ≛[V1] L2 → V1 ≛ V2 → L1.ⓑ{I}V1 ≛[#0] L2.ⓑ{I}V2.
/2 width=1 by rex_pair/ qed.
(*
-lemma rdeq_unit: ∀f,I,L1,L2. 𝐈⦃f⦄ → L1 ⪤[cdeq_ext, cfull, f] L2 →
+lemma rdeq_unit: ∀f,I,L1,L2. 𝐈⦃f⦄ → L1 ⪤[cdeq_ext,cfull,f] L2 →
L1.ⓤ{I} ≛[#0] L2.ⓤ{I}.
/2 width=3 by rex_unit/ qed.
*)
∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
| ∃∃I,L1,L2,V1,V2. L1 ≛[V1] L2 & V1 ≛ V2 &
Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
- | ∃∃f,I,L1,L2. 𝐈⦃f⦄ & L1 ⪤[cdeq_ext h o, cfull, f] L2 &
+ | ∃∃f,I,L1,L2. 𝐈⦃f⦄ & L1 ⪤[cdeq_ext h o,cfull,f] L2 &
Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
#Y1 #Y2 #H elim (rex_inv_zero … H) -H *
/3 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex4_4_intro, conj/