(* Advanved properties ******************************************************)
-lemma crr_append_sn: ∀L,K,T. L ⊢ 𝐑⦃T⦄ → K @@ L ⊢ 𝐑⦃T⦄.
-#L #K0 #T #H elim H -L -T /2 width=1/
+lemma crr_append_sn: ∀G,L,K,T. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → ⦃G, K @@ L⦄ ⊢ 𝐑⦃T⦄.
+#G #L #K0 #T #H elim H -L -T /2 width=1/
#L #K #V #i #HLK
lapply (ldrop_fwd_length_lt2 … HLK) #Hi
lapply (ldrop_O1_append_sn_le … HLK … K0) -HLK /2 width=2/ -Hi /2 width=3/
qed.
-lemma trr_crr: ∀L,T. ⋆ ⊢ 𝐑⦃T⦄ → L ⊢ 𝐑⦃T⦄.
-#L #T #H lapply (crr_append_sn … H) //
+lemma trr_crr: ∀G,L,T. ⦃G, ⋆⦄ ⊢ 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ 𝐑⦃T⦄.
+#G #L #T #H lapply (crr_append_sn … H) //
qed.
(* Advanced inversion lemmas ************************************************)
-fact crr_inv_labst_last_aux: ∀L1,T,W. L1 ⊢ 𝐑⦃T⦄ →
- ∀L2. L1 = ⋆.ⓛW @@ L2 → L2 ⊢ 𝐑⦃T⦄.
-#L1 #T #W #H elim H -L1 -T /2 width=1/ /3 width=1/
+fact crr_inv_labst_last_aux: ∀G,L1,T,W. ⦃G, L1⦄ ⊢ 𝐑⦃T⦄ →
+ ∀L2. L1 = ⋆.ⓛW @@ L2 → ⦃G, L2⦄ ⊢ 𝐑⦃T⦄.
+#G #L1 #T #W #H elim H -L1 -T /2 width=1/ /3 width=1/
[ #L1 #K1 #V1 #i #HLK1 #L2 #H destruct
lapply (ldrop_fwd_length_lt2 … HLK1)
>append_length >commutative_plus normalize in ⊢ (??% → ?); #H
- elim (le_to_or_lt_eq i (|L2|) ?) /2 width=1/ -H #Hi destruct
+ elim (le_to_or_lt_eq i (|L2|)) /2 width=1/ -H #Hi destruct
[ elim (ldrop_O1_lt … Hi) #I2 #K2 #V2 #HLK2
lapply (ldrop_O1_inv_append1_le … HLK1 … HLK2) -HLK1 /2 width=2/ -Hi
normalize #H destruct /2 width=3/
]
qed.
-lemma crr_inv_labst_last: ∀L,T,W. ⋆.ⓛW @@ L ⊢ 𝐑⦃T⦄ → L ⊢ 𝐑⦃T⦄.
+lemma crr_inv_labst_last: ∀G,L,T,W. ⦃G, ⋆.ⓛW @@ L⦄ ⊢ 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ 𝐑⦃T⦄.
/2 width=4/ qed-.
-lemma crr_inv_trr: ∀T,W. ⋆.ⓛW ⊢ 𝐑⦃T⦄ → ⋆ ⊢ 𝐑⦃T⦄.
+lemma crr_inv_trr: ∀G,T,W. ⦃G, ⋆.ⓛW⦄ ⊢ 𝐑⦃T⦄ → ⦃G, ⋆⦄ ⊢ 𝐑⦃T⦄.
/2 width=4/ qed-.