- a comment removed

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / lpss_lpss.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lpss_lpss.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lpss_lpss.ma
index ad972cd4a249a0200c71b7f1e50bfa55d4e88a6b..12bb02b070bdf1837d96bdb61d14f71dbfeb0892 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lpss_lpss.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lpss_lpss.ma
@@ -24,7 +24,7 @@ fact cpss_conf_lpss_atom_atom:
 
 fact cpss_conf_lpss_atom_delta:
    ∀L0,i. (
-      ∀L,T.♯{L, T} < ♯{L0, #i} →
+      ∀L,T. ⦃L0, #i⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ▶* T1 → ∀T2. L ⊢ T ▶* T2 →
       ∀L1. L ⊢ ▶* L1 → ∀L2. L ⊢ ▶* L2 →
       ∃∃T0. L1 ⊢ T1 ▶* T0 & L2 ⊢ T2 ▶* T0
@@ -39,7 +39,7 @@ elim (lpss_inv_pair1 … H1) -H1 #K1 #V1 #HK01 #HV01 #H destruct
 elim (lpss_ldrop_conf … HLK0 … HL02) -HL02 #X2 #H2 #HLK2
 elim (lpss_inv_pair1 … H2) -H2 #K2 #W2 #HK02 #_ #H destruct
 lapply (ldrop_fwd_ldrop2 … HLK2) -W2 #HLK2
-lapply (ldrop_pair2_fwd_fw … HLK0 (#i)) -HLK0 #HLK0
+lapply (fsupp_lref … HLK0) -HLK0 #HLK0
 elim (IH … HLK0 … HV01 … HV02 … HK01 … HK02) -L0 -K0 -V0 #V #HV1 #HV2
 elim (lift_total V 0 (i+1)) #T #HVT
 lapply (cpss_lift … HV2 … HLK2 … HVT2 … HVT) -K2 -V2 /3 width=6/
@@ -47,7 +47,7 @@ qed-.
 
 fact cpss_conf_lpss_delta_delta:
    ∀L0,i. (
-      ∀L,T.♯{L, T} < ♯{L0, #i} →
+      ∀L,T. ⦃L0, #i⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ▶* T1 → ∀T2. L ⊢ T ▶* T2 →
       ∀L1. L ⊢ ▶* L1 → ∀L2. L ⊢ ▶* L2 →
       ∃∃T0. L1 ⊢ T1 ▶* T0 & L2 ⊢ T2 ▶* T0
@@ -67,7 +67,7 @@ lapply (ldrop_fwd_ldrop2 … HLK1) -W1 #HLK1
 elim (lpss_ldrop_conf … HLK0 … HL02) -HL02 #X2 #H2 #HLK2
 elim (lpss_inv_pair1 … H2) -H2 #K2 #W2 #HK02 #_ #H destruct
 lapply (ldrop_fwd_ldrop2 … HLK2) -W2 #HLK2
-lapply (ldrop_pair2_fwd_fw … HLK0 (#i)) -HLK0 #HLK0
+lapply (fsupp_lref … HLK0) -HLK0 #HLK0
 elim (IH … HLK0 … HV01 … HV02 … HK01 … HK02) -L0 -K0 -V0 #V #HV1 #HV2
 elim (lift_total V 0 (i+1)) #T #HVT
 lapply (cpss_lift … HV1 … HLK1 … HVT1 … HVT) -K1 -V1
@@ -76,7 +76,7 @@ qed-.
 
 fact cpss_conf_lpss_bind_bind:
    ∀a,I,L0,V0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓑ{a,I}V0.T0} →
+      ∀L,T. ⦃L0,ⓑ{a,I}V0.T0⦄ ⊃+ ⦃L,T⦄ →
       ∀T1. L ⊢ T ▶* T1 → ∀T2. L ⊢ T ▶* T2 →
       ∀L1. L ⊢ ▶* L1 → ∀L2. L ⊢ ▶* L2 →
       ∃∃T0. L1 ⊢ T1 ▶* T0 & L2 ⊢ T2 ▶* T0
@@ -93,7 +93,7 @@ qed-.
 
 fact cpss_conf_lpss_flat_flat:
    ∀I,L0,V0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓕ{I}V0.T0} →
+      ∀L,T. ⦃L0,ⓕ{I}V0.T0⦄ ⊃+ ⦃L,T⦄ →
       ∀T1. L ⊢ T ▶* T1 → ∀T2. L ⊢ T ▶* T2 →
       ∀L1. L ⊢ ▶* L1 → ∀L2. L ⊢ ▶* L2 →
       ∃∃T0. L1 ⊢ T1 ▶* T0 & L2 ⊢ T2 ▶* T0
@@ -109,8 +109,8 @@ elim (IH … HT01 … HT02 … HL01 … HL02) // /3 width=5/
 qed-.
 
 theorem cpss_conf_lpss: lpx_sn_confluent cpss cpss.
-#L0 #T0 @(f2_ind … fw … L0 T0) -L0 -T0 #n #IH #L0 * [|*]
-[ #I0 #Hn #T1 #H1 #T2 #H2 #L1 #HL01 #L2 #HL02 destruct
+#L0 #T0 @(fsupp_wf_ind … L0 T0) -L0 -T0 #L #T #IH #L0 * [|*]
+[ #I0 #HL #HT #T1 #H1 #T2 #H2 #L1 #HL01 #L2 #HL02 destruct
   elim (cpss_inv_atom1 … H1) -H1
   elim (cpss_inv_atom1 … H2) -H2
   [ #H2 #H1 destruct
@@ -123,11 +123,11 @@ theorem cpss_conf_lpss: lpx_sn_confluent cpss cpss.
     * #K0 #V0 #V1 #i #HLK0 #HV01 #HVT1 #H1 destruct
     /3 width=17 by cpss_conf_lpss_delta_delta/
   ]
-| #a #I #V0 #T0 #Hn #X1 #H1 #X2 #H2 #L1 #HL01 #L2 #HL02 destruct
+| #a #I #V0 #T0 #HL #HT #X1 #H1 #X2 #H2 #L1 #HL01 #L2 #HL02 destruct
   elim (cpss_inv_bind1 … H1) -H1 #V1 #T1 #HV01 #HT01 #H destruct
   elim (cpss_inv_bind1 … H2) -H2 #V2 #T2 #HV02 #HT02 #H destruct
   /3 width=10 by cpss_conf_lpss_bind_bind/
-| #I #V0 #T0 #Hn #X1 #H1 #X2 #H2 #L1 #HL01 #L2 #HL02 destruct
+| #I #V0 #T0 #HL #HT #X1 #H1 #X2 #H2 #L1 #HL01 #L2 #HL02 destruct
   elim (cpss_inv_flat1 … H1) -H1 #V1 #T1 #HV01 #HT01 #H destruct
   elim (cpss_inv_flat1 … H2) -H2 #V2 #T2 #HV02 #HT02 #H destruct
   /3 width=10 by cpss_conf_lpss_flat_flat/