X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Fsubstitution%2Fltps_tps.ma;h=e8dfe59af8fe203579a0f7c46373dde533ca191a;hb=ef3bdc4be26f6518a82a79c64e986253f7aeaa3c;hp=c021f5d5096fb05c9f15f5a7261b114c993f846d;hpb=48e1e9851375f52d26ccba5bf4babd0b3474d869;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps_tps.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps_tps.ma
index c021f5d50..e8dfe59af 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps_tps.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps_tps.ma
@@ -17,94 +17,94 @@ include "Basic_2/substitution/ltps_ldrop.ma".
 
 (* PARALLEL SUBSTITUTION ON LOCAL ENVIRONMENTS ******************************)
 
-lemma ltps_tps_conf_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ≫ U2 →
-                        ∀L1,d1,e1. L0 [d1, e1] ≫ L1 → d1 + e1 ≤ d2 →
-                        L1 ⊢ T2 [d2, e2] ≫ U2.
+lemma ltps_tps_conf_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
+                        ∀L1,d1,e1. L0 [d1, e1] ▶ L1 → d1 + e1 ≤ d2 →
+                        L1 ⊢ T2 [d2, e2] ▶ U2.
 #L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
 [ //
 | #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL01 #Hde1d2
   lapply (transitive_le … Hde1d2 Hdi2) -Hde1d2 #Hde1i2
   lapply (ltps_ldrop_conf_ge … HL01 … HLK0 ?) -L0 // /2 width=4/
 | #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL01 #Hde1d2
-  @tps_bind [ /2 width=4/ | @IHTU2 /2 width=4/ ] (**) (* explicit constructor *)
+  @tps_bind [ /2 width=4/ | @IHTU2 -IHTU2 -IHVW2 [3: /2 by ltps_tps1/ |1,2: skip | /2 width=1/ ] ] (**) (* explicit constructor *)
 | /3 width=4/
 ]
 qed.
 
 (* Basic_1: was: subst1_subst1_back *)
-lemma ltps_tps_conf: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ≫ U2 →
-                     ∀L1,d1,e1. L0 [d1, e1] ≫ L1 →
-                     ∃∃T. L1 ⊢ T2 [d2, e2] ≫ T &
-                          L1 ⊢ U2 [d1, e1] ≫ T.
+lemma ltps_tps_conf: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
+                     ∀L1,d1,e1. L0 [d1, e1] ▶ L1 →
+                     ∃∃T. L1 ⊢ T2 [d2, e2] ▶ T &
+                          L1 ⊢ U2 [d1, e1] ▶ T.
 #L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
 [ /2 width=3/
 | #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL01
   elim (lt_or_ge i2 d1) #Hi2d1
-  [ elim (ltps_ldrop_conf_le … HL01 … HLK0 ?) -L0 /2 width=1/ #X #H #HLK1
+  [ elim (ltps_ldrop_conf_le … HL01 … HLK0 ?) -L0 /2 width=2/ #X #H #HLK1
     elim (ltps_inv_tps11 … H ?) -H /2 width=1/ #K1 #V1 #_ #HV01 #H destruct
     lapply (ldrop_fwd_ldrop2 … HLK1) #H
     elim (lift_total V1 0 (i2 + 1)) #W1 #HVW1
-    lapply (tps_lift_ge … HV01 … H HVW0 HVW1 ?) -V0 -H // >arith_a2 // /3 width=4/
+    lapply (tps_lift_ge … HV01 … H HVW0 HVW1 ?) -V0 -H // >minus_plus <plus_minus_m_m // /3 width=4/
   | elim (lt_or_ge i2 (d1 + e1)) #Hde1i2
-    [ elim (ltps_ldrop_conf_be … HL01 … HLK0 ? ?) -L0 /2 width=1/ #X #H #HLK1
+    [ elim (ltps_ldrop_conf_be … HL01 … HLK0 ? ?) -L0 // /2 width=2/ #X #H #HLK1
       elim (ltps_inv_tps21 … H ?) -H /2 width=1/ #K1 #V1 #_ #HV01 #H destruct
       lapply (ldrop_fwd_ldrop2 … HLK1) #H
       elim (lift_total V1 0 (i2 + 1)) #W1 #HVW1
       lapply (tps_lift_ge … HV01 … H HVW0 HVW1 ?) -V0 -H // normalize #HW01
-      lapply (tps_weak … HW01 d1 e1 ? ?) [2: /2 width=1/ |3: /3 width=4/ ] >arith_i2 //
+      lapply (tps_weak … HW01 d1 e1 ? ?) [2: /2 width=1/ |3: /3 width=4/ ] >minus_plus >commutative_plus /2 width=1/
     | lapply (ltps_ldrop_conf_ge … HL01 … HLK0 ?) -L0 // /3 width=4/
     ]
   ]
 | #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL01
   elim (IHVW2 … HL01) -IHVW2 #V #HV2 #HVW2
-  elim (IHTU2 (L1. 𝕓{I} V) (d1 + 1) e1 ?) -IHTU2 /2 width=1/ -HL01 /3 width=5/
+  elim (IHTU2 (L1. ⓑ{I} V) (d1 + 1) e1 ?) -IHTU2 /2 width=1/ -HL01 /3 width=5/
 | #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL01
   elim (IHVW2 … HL01) -IHVW2
   elim (IHTU2 … HL01) -IHTU2 -HL01 /3 width=5/
 ]
 qed.
 
-lemma ltps_tps_trans_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ≫ U2 →
-                         ∀L1,d1,e1. L1 [d1, e1] ≫ L0 → d1 + e1 ≤ d2 →
-                         L1 ⊢ T2 [d2, e2] ≫ U2.
+lemma ltps_tps_trans_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
+                         ∀L1,d1,e1. L1 [d1, e1] ▶ L0 → d1 + e1 ≤ d2 →
+                         L1 ⊢ T2 [d2, e2] ▶ U2.
 #L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
 [ //
 | #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL10 #Hde1d2
   lapply (transitive_le … Hde1d2 Hdi2) -Hde1d2 #Hde1i2
   lapply (ltps_ldrop_trans_ge … HL10 … HLK0 ?) -L0 // /2 width=4/
 | #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL10 #Hde1d2
-  @tps_bind [ /2 width=4/ | @IHTU2 /2 width=4/ ] (**) (* explicit constructor *)
+  @tps_bind [ /2 width=4/ | @IHTU2 -IHTU2 -IHVW2 [3: /2 by ltps_tps1/ |1,2: skip | /2 width=1/ ] ] (**) (* explicit constructor *)
 | /3 width=4/
 ]
 qed.
 
 (* Basic_1: was: subst1_subst1 *)
-lemma ltps_tps_trans: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ≫ U2 →
-                      ∀L1,d1,e1. L1 [d1, e1] ≫ L0 →
-                      ∃∃T. L1 ⊢ T2 [d2, e2] ≫ T &
-                           L0 ⊢ T [d1, e1] ≫ U2.
+lemma ltps_tps_trans: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
+                      ∀L1,d1,e1. L1 [d1, e1] ▶ L0 →
+                      ∃∃T. L1 ⊢ T2 [d2, e2] ▶ T &
+                           L0 ⊢ T [d1, e1] ▶ U2.
 #L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
 [ /2 width=3/
 | #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL10
   elim (lt_or_ge i2 d1) #Hi2d1
-  [ elim (ltps_ldrop_trans_le … HL10 … HLK0 ?) -HL10 /2 width=1/ #X #H #HLK1
+  [ elim (ltps_ldrop_trans_le … HL10 … HLK0 ?) -HL10 /2 width=2/ #X #H #HLK1
     elim (ltps_inv_tps12 … H ?) -H /2 width=1/ #K1 #V1 #_ #HV01 #H destruct
     lapply (ldrop_fwd_ldrop2 … HLK0) -HLK0 #H
     elim (lift_total V1 0 (i2 + 1)) #W1 #HVW1
-    lapply (tps_lift_ge … HV01 … H HVW1 HVW0 ?) -V0 -H // >arith_a2 // /3 width=4/
+    lapply (tps_lift_ge … HV01 … H HVW1 HVW0 ?) -V0 -H // >minus_plus <plus_minus_m_m /2 width=1/ /3 width=4/
   | elim (lt_or_ge i2 (d1 + e1)) #Hde1i2
-    [ elim (ltps_ldrop_trans_be … HL10 … HLK0 ? ?) -HL10 // /2 width=1/ #X #H #HLK1
+    [ elim (ltps_ldrop_trans_be … HL10 … HLK0 ? ?) -HL10 // /2 width=2/ #X #H #HLK1
       elim (ltps_inv_tps22 … H ?) -H /2 width=1/ #K1 #V1 #_ #HV01 #H destruct
       lapply (ldrop_fwd_ldrop2 … HLK0) -HLK0 #H
       elim (lift_total V1 0 (i2 + 1)) #W1 #HVW1
       lapply (tps_lift_ge … HV01 … H HVW1 HVW0 ?) -V0 -H // normalize #HW01
-      lapply (tps_weak … HW01 d1 e1 ? ?) [2: /3 width=1/ |3: /3 width=4/ ] >arith_i2 //
+      lapply (tps_weak … HW01 d1 e1 ? ?) [2: /3 width=1/ |3: /3 width=4/ ] >minus_plus >commutative_plus /2 width=1/
     | lapply (ltps_ldrop_trans_ge … HL10 … HLK0 ?) -HL10 -HLK0 // /3 width=4/
     ]
   ]
 | #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL10
   elim (IHVW2 … HL10) -IHVW2 #V #HV2 #HVW2
-  elim (IHTU2 (L1. 𝕓{I} V) (d1 + 1) e1 ?) -IHTU2 /2 width=1/ -HL10 /3 width=5/
+  elim (IHTU2 (L1. ⓑ{I} V) (d1 + 1) e1 ?) -IHTU2 /2 width=1/ -HL10 /3 width=5/
 | #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL10
   elim (IHVW2 … HL10) -IHVW2
   elim (IHTU2 … HL10) -IHTU2 -HL10 /3 width=5/