-lemma cpcs_bind2: ∀a,I,L,V1,V2. L ⊢ V1 ⬌* V2 → ∀T1,T2. L.ⓑ{I}V2 ⊢ T1 ⬌* T2 →
- L ⊢ ⓑ{a,I}V1. T1 ⬌* ⓑ{a,I}V2. T2.
-#a #I #L #V1 #V2 #HV12 #T1 #T2 #HT12
-@(cpcs_trans … (ⓑ{a,I}V2.T1)) /2 width=1/
-qed.
-
-lemma cpcs_beta_dx: ∀a,L,V1,V2,W1,W2,T1,T2.
- L ⊢ V1 ⬌* V2 → L ⊢ W1 ⬌* W2 → L.ⓛW2 ⊢ T1 ⬌* T2 →
- L ⊢ ⓐV1.ⓛ{a}W1.T1 ⬌* ⓓ{a}ⓝW2.V2.T2.
-#a #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #HT12
-@(cpcs_cpr_strap1 … (ⓐV2.ⓛ{a}W2.T2)) /2 width=1/ /3 width=1/
-qed.
-
-lemma cpcs_beta_sn: ∀a,L,V1,V2,W1,W2,T1,T2.
- L ⊢ V1 ⬌* V2 → L ⊢ W1 ⬌* W2 → L.ⓛW1 ⊢ T1 ⬌* T2 →
- L ⊢ ⓐV1.ⓛ{a}W1.T1 ⬌* ⓓ{a}ⓝW2.V2.T2.
-#a #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #HT12
-lapply (lsubx_cpcs_trans … HT12 (L.ⓓⓝW1.V1) ?) /2 width=1/ #H2T12
-@(cpcs_cpr_strap2 … (ⓓ{a}ⓝW1.V1.T1)) /2 width=1/ -HT12 /3 width=1/
-qed.
+lemma cpcs_bind2: ∀a,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 →
+ ∀T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬌* T2 →
+ ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T1 ⬌* ⓑ{a,I}V2. T2.
+/3 width=3 by cpcs_trans, cpcs_bind_sn, cpcs_bind_dx/ qed.