- main lemmas about abstract reducibility candidates closed

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / substitution / ltps.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps.ma
index 9adf787100d1d1ca509bd35268a8223a9871b05c..9f5547ed03dcaf13ce00c3c5d59c138992beafcd 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps.ma
@@ -19,13 +19,13 @@ include "Basic_2/substitution/tps.ma".
 (* Basic_1: includes: csubst1_bind *)
 inductive ltps: nat → nat → relation lenv ≝
 | ltps_atom: ∀d,e. ltps d e (⋆) (⋆)
-| ltps_pair: ∀L,I,V. ltps 0 0 (L. 𝕓{I} V) (L. 𝕓{I} V)
+| ltps_pair: ∀L,I,V. ltps 0 0 (L. ⓑ{I} V) (L. ⓑ{I} V)
 | ltps_tps2: ∀L1,L2,I,V1,V2,e.
              ltps 0 e L1 L2 → L2 ⊢ V1 [0, e] ▶ V2 →
-             ltps 0 (e + 1) (L1. 𝕓{I} V1) L2. 𝕓{I} V2
+             ltps 0 (e + 1) (L1. ⓑ{I} V1) L2. ⓑ{I} V2
 | ltps_tps1: ∀L1,L2,I,V1,V2,d,e.
              ltps d e L1 L2 → L2 ⊢ V1 [d, e] ▶ V2 →
-             ltps (d + 1) e (L1. 𝕓{I} V1) (L2. 𝕓{I} V2)
+             ltps (d + 1) e (L1. ⓑ{I} V1) (L2. ⓑ{I} V2)
 .
 
 interpretation "parallel substritution (local environment)"
@@ -35,14 +35,14 @@ interpretation "parallel substritution (local environment)"
 
 lemma ltps_tps2_lt: ∀L1,L2,I,V1,V2,e.
                     L1 [0, e - 1] ▶ L2 → L2 ⊢ V1 [0, e - 1] ▶ V2 →
-                    0 < e → L1. 𝕓{I} V1 [0, e] ▶ L2. 𝕓{I} V2.
+                    0 < e → L1. ⓑ{I} V1 [0, e] ▶ L2. ⓑ{I} V2.
 #L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #He
 >(plus_minus_m_m e 1) /2 width=1/
 qed.
 
 lemma ltps_tps1_lt: ∀L1,L2,I,V1,V2,d,e.
                     L1 [d - 1, e] ▶ L2 → L2 ⊢ V1 [d - 1, e] ▶ V2 →
-                    0 < d → L1. 𝕓{I} V1 [d, e] ▶ L2. 𝕓{I} V2.
+                    0 < d → L1. ⓑ{I} V1 [d, e] ▶ L2. ⓑ{I} V2.
 #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #Hd
 >(plus_minus_m_m d 1) /2 width=1/
 qed.
@@ -80,10 +80,10 @@ lemma ltps_inv_atom1: ∀d,e,L2. ⋆ [d, e] ▶ L2 → L2 = ⋆.
 /2 width=5/ qed-.
 
 fact ltps_inv_tps21_aux: ∀d,e,L1,L2. L1 [d, e] ▶ L2 → d = 0 → 0 < e →
-                         ∀K1,I,V1. L1 = K1. 𝕓{I} V1 →
+                         ∀K1,I,V1. L1 = K1. ⓑ{I} V1 →
                          ∃∃K2,V2. K1 [0, e - 1] ▶ K2 &
                                   K2 ⊢ V1 [0, e - 1] ▶ V2 &
-                                  L2 = K2. 𝕓{I} V2.
+                                  L2 = K2. ⓑ{I} V2.
 #d #e #L1 #L2 * -d -e -L1 -L2
 [ #d #e #_ #_ #K1 #I #V1 #H destruct
 | #L1 #I #V #_ #H elim (lt_refl_false … H)
@@ -92,16 +92,16 @@ fact ltps_inv_tps21_aux: ∀d,e,L1,L2. L1 [d, e] ▶ L2 → d = 0 → 0 < e →
 ]
 qed.
 
-lemma ltps_inv_tps21: ∀e,K1,I,V1,L2. K1. 𝕓{I} V1 [0, e] ▶ L2 → 0 < e →
+lemma ltps_inv_tps21: ∀e,K1,I,V1,L2. K1. ⓑ{I} V1 [0, e] ▶ L2 → 0 < e →
                       ∃∃K2,V2. K1 [0, e - 1] ▶ K2 & K2 ⊢ V1 [0, e - 1] ▶ V2 &
-                               L2 = K2. 𝕓{I} V2.
+                               L2 = K2. ⓑ{I} V2.
 /2 width=5/ qed-.
 
 fact ltps_inv_tps11_aux: ∀d,e,L1,L2. L1 [d, e] ▶ L2 → 0 < d →
-                         ∀I,K1,V1. L1 = K1. 𝕓{I} V1 →
+                         ∀I,K1,V1. L1 = K1. ⓑ{I} V1 →
                          ∃∃K2,V2. K1 [d - 1, e] ▶ K2 &
                                   K2 ⊢ V1 [d - 1, e] ▶ V2 &
-                                  L2 = K2. 𝕓{I} V2.
+                                  L2 = K2. ⓑ{I} V2.
 #d #e #L1 #L2 * -d -e -L1 -L2
 [ #d #e #_ #I #K1 #V1 #H destruct
 | #L #I #V #H elim (lt_refl_false … H)
@@ -110,10 +110,10 @@ fact ltps_inv_tps11_aux: ∀d,e,L1,L2. L1 [d, e] ▶ L2 → 0 < d →
 ]
 qed.
 
-lemma ltps_inv_tps11: ∀d,e,I,K1,V1,L2. K1. 𝕓{I} V1 [d, e] ▶ L2 → 0 < d →
+lemma ltps_inv_tps11: ∀d,e,I,K1,V1,L2. K1. ⓑ{I} V1 [d, e] ▶ L2 → 0 < d →
                       ∃∃K2,V2. K1 [d - 1, e] ▶ K2 &
                                   K2 ⊢ V1 [d - 1, e] ▶ V2 &
-                                  L2 = K2. 𝕓{I} V2.
+                                  L2 = K2. ⓑ{I} V2.
 /2 width=3/ qed-.
 
 fact ltps_inv_atom2_aux: ∀d,e,L1,L2.
@@ -130,10 +130,10 @@ lemma ltps_inv_atom2: ∀d,e,L1. L1 [d, e] ▶ ⋆ → L1 = ⋆.
 /2 width=5/ qed-.
 
 fact ltps_inv_tps22_aux: ∀d,e,L1,L2. L1 [d, e] ▶ L2 → d = 0 → 0 < e →
-                         ∀K2,I,V2. L2 = K2. 𝕓{I} V2 →
+                         ∀K2,I,V2. L2 = K2. ⓑ{I} V2 →
                          ∃∃K1,V1. K1 [0, e - 1] ▶ K2 &
                                   K2 ⊢ V1 [0, e - 1] ▶ V2 &
-                                  L1 = K1. 𝕓{I} V1.
+                                  L1 = K1. ⓑ{I} V1.
 #d #e #L1 #L2 * -d -e -L1 -L2
 [ #d #e #_ #_ #K1 #I #V1 #H destruct
 | #L1 #I #V #_ #H elim (lt_refl_false … H)
@@ -142,16 +142,16 @@ fact ltps_inv_tps22_aux: ∀d,e,L1,L2. L1 [d, e] ▶ L2 → d = 0 → 0 < e →
 ]
 qed.
 
-lemma ltps_inv_tps22: ∀e,L1,K2,I,V2. L1 [0, e] ▶ K2. 𝕓{I} V2 → 0 < e →
+lemma ltps_inv_tps22: ∀e,L1,K2,I,V2. L1 [0, e] ▶ K2. ⓑ{I} V2 → 0 < e →
                       ∃∃K1,V1. K1 [0, e - 1] ▶ K2 & K2 ⊢ V1 [0, e - 1] ▶ V2 &
-                               L1 = K1. 𝕓{I} V1.
+                               L1 = K1. ⓑ{I} V1.
 /2 width=5/ qed-.
 
 fact ltps_inv_tps12_aux: ∀d,e,L1,L2. L1 [d, e] ▶ L2 → 0 < d →
-                         ∀I,K2,V2. L2 = K2. 𝕓{I} V2 →
+                         ∀I,K2,V2. L2 = K2. ⓑ{I} V2 →
                          ∃∃K1,V1. K1 [d - 1, e] ▶ K2 &
                                   K2 ⊢ V1 [d - 1, e] ▶ V2 &
-                                  L1 = K1. 𝕓{I} V1.
+                                  L1 = K1. ⓑ{I} V1.
 #d #e #L1 #L2 * -d -e -L1 -L2
 [ #d #e #_ #I #K2 #V2 #H destruct
 | #L #I #V #H elim (lt_refl_false … H)
@@ -160,10 +160,10 @@ fact ltps_inv_tps12_aux: ∀d,e,L1,L2. L1 [d, e] ▶ L2 → 0 < d →
 ]
 qed.
 
-lemma ltps_inv_tps12: ∀L1,K2,I,V2,d,e. L1 [d, e] ▶ K2. 𝕓{I} V2 → 0 < d →
+lemma ltps_inv_tps12: ∀L1,K2,I,V2,d,e. L1 [d, e] ▶ K2. ⓑ{I} V2 → 0 < d →
                       ∃∃K1,V1. K1 [d - 1, e] ▶ K2 &
                                   K2 ⊢ V1 [d - 1, e] ▶ V2 &
-                                  L1 = K1. 𝕓{I} V1.
+                                  L1 = K1. ⓑ{I} V1.
 /2 width=3/ qed-.
 
 (* Basic_1: removed theorems 27: