- revision of ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / frees_append.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/frees_append.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/frees_append.ma
index 8f683595597b0cbb9edeafb311494d755fb5c4b5..ee8324cc9c30d2288eeb1bb6408e5a303cf6e655 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/frees_append.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/frees_append.ma
@@ -25,9 +25,10 @@ lemma frees_append: ∀L2,U,l,i. L2 ⊢ i ϵ 𝐅*[l]⦃U⦄ → i ≤ |L2| →
 #I #L2 #K2 #U #W #l #i #j #Hlj #Hji #HnU #HLK2 #_ #IHW #Hi #L1
 lapply (drop_fwd_length_minus2 … HLK2) normalize #H0
 lapply (drop_O1_append_sn_le … HLK2 … L1) -HLK2
-[ -I -L1 -K2 -U -W -l /3 width=3 by lt_to_le, lt_to_le_to_lt/
+[ -I -L1 -K2 -U -W -l /4 width=3 by ylt_yle_trans, ylt_inv_inj, lt_to_le/
 | #HLK2 @(frees_be … HnU HLK2) // -HnU -HLK2 @IHW -IHW
-  >(minus_plus_m_m (|K2|) 1) >H0 -H0 /2 width=1 by monotonic_le_minus_l2/
+  >(minus_plus_m_m (|K2|) 1) >H0 -H0 <yminus_inj >yminus_SO2
+  /3 width=1 by monotonic_yle_minus_dx, yle_pred/
 ]
 qed.
 
@@ -37,13 +38,14 @@ fact frees_inv_append_aux: ∀L,U,l,i. L ⊢ i ϵ 𝐅*[l]⦃U⦄ → ∀L1,L2.
                            i ≤ |L2| → L2 ⊢ i ϵ 𝐅*[l]⦃U⦄.
 #L #U #l #i #H elim H -L -U -l -i /3 width=2 by frees_eq/
 #Z #L #Y #U #X #l #i #j #Hlj #Hji #HnU #HLY #_ #IHW #L1 #L2 #H #Hi destruct
-elim (drop_O1_lt (Ⓕ) L2 j) [2: -Z -Y -L1 -X -U -l /2 width=3 by lt_to_le_to_lt/ ]
+elim (drop_O1_lt (Ⓕ) L2 j) [2: -Z -Y -L1 -X -U -l /3 width=3 by ylt_yle_trans, ylt_inv_inj/ ]
 #I #K2 #W #HLK2 lapply (drop_fwd_length_minus2 … HLK2) normalize #H0
 lapply (drop_O1_inv_append1_le … HLY … HLK2) -HLY
-[ -Z -I -Y -K2 -L1 -X -U -W -l /3 width=3 by lt_to_le, lt_to_le_to_lt/
+[ -Z -I -Y -K2 -L1 -X -U -W -l /4 width=3 by ylt_yle_trans, ylt_inv_inj, lt_to_le/
 | normalize #H destruct
   @(frees_be … HnU HLK2) -HnU -HLK2 // @IHW -IHW //
-  >(minus_plus_m_m (|K2|) 1) >H0 -H0 /2 width=1 by monotonic_le_minus_l2/
+  >(minus_plus_m_m (|K2|) 1) >H0 -H0 <yminus_inj >yminus_SO2
+  /3 width=1 by monotonic_yle_minus_dx, yle_pred/
 ]
 qed-.