(* Basic inversion lemmas ***************************************************)
-fact lsuba_inv_atom1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → L1 = ⋆ → L2 = ⋆.
+fact lsuba_inv_atom1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → L1 = ⋆ → L2 = ⋆.
#G #L1 #L2 * -L1 -L2
[ //
| #I #L1 #L2 #V #_ #H destruct
]
qed-.
-lemma lsuba_inv_atom1: â\88\80G,L2. G â\8a¢ â\8b\86 â\81\9dâ\8a\91 L2 → L2 = ⋆.
+lemma lsuba_inv_atom1: â\88\80G,L2. G â\8a¢ â\8b\86 â\81\9dâ«\83 L2 → L2 = ⋆.
/2 width=4 by lsuba_inv_atom1_aux/ qed-.
-fact lsuba_inv_pair1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
- (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & L2 = K2.ⓑ{I}X) ∨
+fact lsuba_inv_pair1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
+ (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ«\83 K2 & L2 = K2.ⓑ{I}X) ∨
∃∃K2,W,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
- G â\8a¢ K1 â\81\9dâ\8a\91 K2 & I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
+ G â\8a¢ K1 â\81\9dâ«\83 K2 & I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
#G #L1 #L2 * -L1 -L2
[ #J #K1 #X #H destruct
| #I #L1 #L2 #V #HL12 #J #K1 #X #H destruct /3 width=3/
]
qed-.
-lemma lsuba_inv_pair1: â\88\80I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â\81\9dâ\8a\91 L2 →
- (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & L2 = K2.ⓑ{I}X) ∨
- â\88\83â\88\83K2,W,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ\8a\91 K2 &
+lemma lsuba_inv_pair1: â\88\80I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â\81\9dâ«\83 L2 →
+ (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ«\83 K2 & L2 = K2.ⓑ{I}X) ∨
+ â\88\83â\88\83K2,W,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ«\83 K2 &
I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
/2 width=3 by lsuba_inv_pair1_aux/ qed-.
-fact lsuba_inv_atom2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → L2 = ⋆ → L1 = ⋆.
+fact lsuba_inv_atom2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → L2 = ⋆ → L1 = ⋆.
#G #L1 #L2 * -L1 -L2
[ //
| #I #L1 #L2 #V #_ #H destruct
]
qed-.
-lemma lsubc_inv_atom2: â\88\80G,L1. G â\8a¢ L1 â\81\9dâ\8a\91 ⋆ → L1 = ⋆.
+lemma lsubc_inv_atom2: â\88\80G,L1. G â\8a¢ L1 â\81\9dâ«\83 ⋆ → L1 = ⋆.
/2 width=4 by lsuba_inv_atom2_aux/ qed-.
-fact lsuba_inv_pair2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → ∀I,K2,W. L2 = K2.ⓑ{I}W →
- (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & L1 = K1.ⓑ{I}W) ∨
+fact lsuba_inv_pair2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀I,K2,W. L2 = K2.ⓑ{I}W →
+ (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ«\83 K2 & L1 = K1.ⓑ{I}W) ∨
∃∃K1,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
- G â\8a¢ K1 â\81\9dâ\8a\91 K2 & I = Abst & L1 = K1.ⓓⓝW.V.
+ G â\8a¢ K1 â\81\9dâ«\83 K2 & I = Abst & L1 = K1.ⓓⓝW.V.
#G #L1 #L2 * -L1 -L2
[ #J #K2 #U #H destruct
| #I #L1 #L2 #V #HL12 #J #K2 #U #H destruct /3 width=3/
]
qed-.
-lemma lsuba_inv_pair2: â\88\80I,G,L1,K2,W. G â\8a¢ L1 â\81\9dâ\8a\91 K2.ⓑ{I}W →
- (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & L1 = K1.ⓑ{I}W) ∨
- â\88\83â\88\83K1,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ\8a\91 K2 &
+lemma lsuba_inv_pair2: â\88\80I,G,L1,K2,W. G â\8a¢ L1 â\81\9dâ«\83 K2.ⓑ{I}W →
+ (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ«\83 K2 & L1 = K1.ⓑ{I}W) ∨
+ â\88\83â\88\83K1,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ«\83 K2 &
I = Abst & L1 = K1.ⓓⓝW.V.
/2 width=3 by lsuba_inv_pair2_aux/ qed-.
(* Basic forward lemmas *****************************************************)
-lemma lsuba_fwd_lsubr: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 â\86\92 L1 â\8a\91 L2.
+lemma lsuba_fwd_lsubr: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 â\86\92 L1 â«\83 L2.
#G #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
qed-.
(* Basic properties *********************************************************)
-lemma lsuba_refl: â\88\80G,L. G â\8a¢ L â\81\9dâ\8a\91 L.
+lemma lsuba_refl: â\88\80G,L. G â\8a¢ L â\81\9dâ«\83 L.
#G #L elim L -L // /2 width=1/
qed.