-lemma cpcs_cpr_conf: ∀L,T1,T. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
-/3 width=3/ qed.
-
-lemma cpcs_cpss_strap1: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T ▶* T2 → L ⊢ T1 ⬌* T2.
-#L #T1 #T #HT1 #T2 #HT2
-@(cpcs_cpr_strap1 … HT1) -T1 /2 width=3/
-qed-.
-
-lemma cpcs_cpss_conf: ∀L,T,T1. L ⊢ T ▶* T1 → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
-#L #T #T1 #HT1 #T2 #HT2
-@(cpcs_cpr_conf … HT2) -T2 /2 width=3/
-qed-.
+lemma cpcs_cpr_conf: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+/3 width=3 by cpcs_strap2, or_intror/ qed-.