update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / lveq.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/lveq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/lveq.ma
index a895a58112277d5adb3bec01e88b9fa6f8873959..776affc1c95b4f3fda5e8dddb22ef4bb39424c59 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/lveq.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/lveq.ma
@@ -22,7 +22,7 @@ include "static_2/syntax/lenv.ma".
 inductive lveq: bi_relation nat lenv ≝
 | lveq_atom   : lveq 0 (⋆) 0 (⋆)
 | lveq_bind   : ∀I1,I2,K1,K2. lveq 0 K1 0 K2 →
-                lveq 0 (K1.ⓘ{I1}) 0 (K2.ⓘ{I2})
+                lveq 0 (K1.ⓘ[I1]) 0 (K2.ⓘ[I2])
 | lveq_void_sn: ∀K1,K2,n1. lveq n1 K1 0 K2 →
                 lveq (↑n1) (K1.ⓧ) 0 K2
 | lveq_void_dx: ∀K1,K2,n2. lveq 0 K1 n2 K2 →
@@ -48,7 +48,7 @@ qed-.
 fact lveq_inv_zero_aux: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
                         0 = n1 → 0 = n2 →
                         ∨∨ ∧∧ ⋆ = L1 & ⋆ = L2
-                            | ∃∃I1,I2,K1,K2. K1 ≋ⓧ*[0,0] K2 & K1.ⓘ{I1} = L1 & K2.ⓘ{I2} = L2.
+                            | ∃∃I1,I2,K1,K2. K1 ≋ⓧ*[0,0] K2 & K1.ⓘ[I1] = L1 & K2.ⓘ[I2] = L2.
 #L1 #L2 #n1 #n2 * -L1 -L2 -n1 -n2
 [1: /3 width=1 by or_introl, conj/
 |2: /3 width=7 by ex3_4_intro, or_intror/
@@ -58,7 +58,7 @@ qed-.
 
 lemma lveq_inv_zero: ∀L1,L2. L1 ≋ⓧ*[0,0] L2 →
                      ∨∨ ∧∧ ⋆ = L1 & ⋆ = L2
-                      | ∃∃I1,I2,K1,K2. K1 ≋ⓧ*[0,0] K2 & K1.ⓘ{I1} = L1 & K2.ⓘ{I2} = L2.
+                      | ∃∃I1,I2,K1,K2. K1 ≋ⓧ*[0,0] K2 & K1.ⓘ[I1] = L1 & K2.ⓘ[I2] = L2.
 /2 width=5 by lveq_inv_zero_aux/ qed-.
 
 fact lveq_inv_succ_sn_aux: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
@@ -96,7 +96,7 @@ lemma lveq_inv_succ: ∀L1,L2,n1,n2. L1 ≋ⓧ*[↑n1,↑n2] L2 → ⊥.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma lveq_inv_bind: ∀I1,I2,K1,K2. K1.ⓘ{I1} ≋ⓧ*[0,0] K2.ⓘ{I2} → K1 ≋ⓧ*[0,0] K2.
+lemma lveq_inv_bind: ∀I1,I2,K1,K2. K1.ⓘ[I1] ≋ⓧ*[0,0] K2.ⓘ[I2] → K1 ≋ⓧ*[0,0] K2.
 #I1 #I2 #K1 #K2 #H
 elim (lveq_inv_zero … H) -H * [| #Z1 #Z2 #Y1 #Y2 #HY ] #H1 #H2 destruct //
 qed-.
@@ -110,7 +110,7 @@ lemma lveq_inv_atom_atom: ∀n1,n2. ⋆ ≋ⓧ*[n1,n2] ⋆ → ∧∧ 0 = n1 & 0
 ]
 qed-.
 
-lemma lveq_inv_bind_atom: ∀I1,K1,n1,n2. K1.ⓘ{I1} ≋ⓧ*[n1,n2] ⋆ →
+lemma lveq_inv_bind_atom: ∀I1,K1,n1,n2. K1.ⓘ[I1] ≋ⓧ*[n1,n2] ⋆ →
                           ∃∃m1. K1 ≋ⓧ*[m1,0] ⋆ & BUnit Void = I1 & ↑m1 = n1 & 0 = n2.
 #I1 #K1 * [2: #n1 ] * [2,4: #n2 ] #H
 [ elim (lveq_inv_succ … H)
@@ -123,7 +123,7 @@ lemma lveq_inv_bind_atom: ∀I1,K1,n1,n2. K1.ⓘ{I1} ≋ⓧ*[n1,n2] ⋆ →
 ]
 qed-.
 
-lemma lveq_inv_atom_bind: ∀I2,K2,n1,n2. ⋆ ≋ⓧ*[n1,n2] K2.ⓘ{I2} →
+lemma lveq_inv_atom_bind: ∀I2,K2,n1,n2. ⋆ ≋ⓧ*[n1,n2] K2.ⓘ[I2] →
                           ∃∃m2. ⋆ ≋ⓧ*[0,m2] K2 & BUnit Void = I2 & 0 = n1 & ↑m2 = n2.
 #I2 #K2 #n1 #n2 #H
 lapply (lveq_sym … H) -H #H
@@ -131,7 +131,7 @@ elim (lveq_inv_bind_atom … H) -H
 /3 width=3 by lveq_sym, ex4_intro/
 qed-.
 
-lemma lveq_inv_pair_pair: ∀I1,I2,K1,K2,V1,V2,n1,n2. K1.ⓑ{I1}V1 ≋ⓧ*[n1,n2] K2.ⓑ{I2}V2 →
+lemma lveq_inv_pair_pair: ∀I1,I2,K1,K2,V1,V2,n1,n2. K1.ⓑ[I1]V1 ≋ⓧ*[n1,n2] K2.ⓑ[I2]V2 →
                           ∧∧ K1 ≋ⓧ*[0,0] K2 & 0 = n1 & 0 = n2.
 #I1 #I2 #K1 #K2 #V1 #V2 * [2: #n1 ] * [2,4: #n2 ] #H
 [ elim (lveq_inv_succ … H)
@@ -167,12 +167,12 @@ lemma lveq_fwd_gen: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
 /2 width=1 by or_introl, or_intror/
 qed-.
 
-lemma lveq_fwd_pair_sn: ∀I1,K1,L2,V1,n1,n2. K1.ⓑ{I1}V1 ≋ⓧ*[n1,n2] L2 → 0 = n1.
+lemma lveq_fwd_pair_sn: ∀I1,K1,L2,V1,n1,n2. K1.ⓑ[I1]V1 ≋ⓧ*[n1,n2] L2 → 0 = n1.
 #I1 #K1 #L2 #V1 * [2: #n1 ] // * [2: #n2 ] #H
 [ elim (lveq_inv_succ … H)
 | elim (lveq_inv_succ_sn … H) -H #Y #_ #H1 #H2 destruct
 ]
 qed-.
 
-lemma lveq_fwd_pair_dx: ∀I2,L1,K2,V2,n1,n2. L1 ≋ⓧ*[n1,n2] K2.ⓑ{I2}V2 → 0 = n2.
+lemma lveq_fwd_pair_dx: ∀I2,L1,K2,V2,n1,n2. L1 ≋ⓧ*[n1,n2] K2.ⓑ[I2]V2 → 0 = n2.
 /3 width=6 by lveq_fwd_pair_sn, lveq_sym/ qed-.