-lemma cprs_inv_abst: ∀a,G,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ➡* ⓛ{a}W2.T2 →
- ⦃G, L⦄ ⊢ W1 ➡* W2 ∧ ⦃G, L.ⓛW1⦄ ⊢ T1 ➡* T2.
-#a #G #L #W1 #W2 #T1 #T2 #H elim (cprs_inv_abst1 … H) -H
-#W #T #HW1 #HT1 #H destruct /2 width=1 by conj/
-qed-.
-
-(* Basic_1: was pr3_gen_abbr *)
-lemma cprs_inv_abbr1: ∀a,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{a}V1.T1 ➡* U2 → (
- ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡* V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ➡* T2 &
- U2 = ⓓ{a}V2.T2
- ) ∨
- ∃∃T2. ⦃G, L.ⓓV1⦄ ⊢ T1 ➡* T2 & ⬆[0, 1] U2 ≡ T2 & a = true.
-#a #G #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/
-#U0 #U2 #_ #HU02 * *
-[ #V0 #T0 #HV10 #HT10 #H destruct
- elim (cpr_inv_abbr1 … HU02) -HU02 *
- [ #V2 #T2 #HV02 #HT02 #H destruct
- lapply (lprs_cpr_trans … HT02 (L.ⓓV1) ?)
- /4 width=5 by lprs_pair, cprs_trans, cprs_strap1, ex3_2_intro, or_introl/
- | #T2 #HT02 #HUT2
- lapply (lprs_cpr_trans … HT02 (L.ⓓV1) ?) -HT02
- /4 width=3 by lprs_pair, cprs_trans, ex3_intro, or_intror/
- ]
-| #U1 #HTU1 #HU01 elim (lift_total U2 0 1)
- #U #HU2 lapply (cpr_lift … HU02 (L.ⓓV1) … HU01 … HU2) -U0
- /4 width=3 by cprs_strap1, drop_drop, ex3_intro, or_intror/
-]
-qed-.
-
-(* More advanced properties *************************************************)
-
-lemma lprs_pair2: ∀I,G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 →
- ∀V1,V2. ⦃G, L2⦄ ⊢ V1 ➡* V2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡* L2.ⓑ{I}V2.
-/3 width=3 by lprs_pair, lprs_cprs_trans/ qed.
+lemma lprs_cpr_conf_sn (h) (G): ∀L0. ∀T0,T1:term. ⦃G, L0⦄ ⊢ T0 ➡[h] T1 →
+ ∀L1. ⦃G, L0⦄ ⊢ ➡*[h] L1 →
+ ∃∃T. ⦃G, L0⦄ ⊢ T1 ➡*[h] T & ⦃G, L1⦄ ⊢ T0 ➡*[h] T.
+/3 width=3 by lprs_cprs_conf_sn, cpm_cpms/ qed-.