component "substitution" updated to new syntax ...

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

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma
index 5bc36f943ededfbe6e9578acc3972cd0e034b4e7..2f92251bd26699324cfb9cecc1f4edadf7349577 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma
@@ -20,19 +20,19 @@ include "Basic_2/substitution/lift.ma".
 
 (* Basic_1: was: lift_inj *)
 theorem lift_inj:  ∀d,e,T1,U. ↑[d,e] T1 ≡ U → ∀T2. ↑[d,e] T2 ≡ U → T1 = T2.
-#d #e #T1 #U #H elim H -H d e T1 U
+#d #e #T1 #U #H elim H -d -e -T1 -U
 [ #k #d #e #X #HX
   lapply (lift_inv_sort2 … HX) -HX //
-| #i #d #e #Hid #X #HX 
+| #i #d #e #Hid #X #HX
   lapply (lift_inv_lref2_lt … HX ?) -HX //
-| #i #d #e #Hdi #X #HX 
-  lapply (lift_inv_lref2_ge … HX ?) -HX /2/
+| #i #d #e #Hdi #X #HX
+  lapply (lift_inv_lref2_ge … HX ?) -HX // /2 width=1/
 | #p #d #e #X #HX
   lapply (lift_inv_gref2 … HX) -HX //
 | #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_bind2 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/
+  elim (lift_inv_bind2 … HX) -HX #V #T #HV1 #HT1 #HX destruct /3 width=1/
 | #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_flat2 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/
+  elim (lift_inv_flat2 … HX) -HX #V #T #HV1 #HT1 #HX destruct /3 width=1/
 ]
 qed-.
 
@@ -41,36 +41,36 @@ theorem lift_div_le: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
                      ∀d2,e2,T2. ↑[d2 + e1, e2] T2 ≡ T →
                      d1 ≤ d2 →
                      ∃∃T0. ↑[d1, e1] T0 ≡ T2 & ↑[d2, e2] T0 ≡ T1.
-#d1 #e1 #T1 #T #H elim H -H d1 e1 T1 T
+#d1 #e1 #T1 #T #H elim H -d1 -e1 -T1 -T
 [ #k #d1 #e1 #d2 #e2 #T2 #Hk #Hd12
-  lapply (lift_inv_sort2 … Hk) -Hk #Hk destruct -T2 /3/
+  lapply (lift_inv_sort2 … Hk) -Hk #Hk destruct /3 width=3/
 | #i #d1 #e1 #Hid1 #d2 #e2 #T2 #Hi #Hd12
   lapply (lt_to_le_to_lt … Hid1 Hd12) -Hd12 #Hid2
-  lapply (lift_inv_lref2_lt … Hi ?) -Hi /2/ /3/
+  lapply (lift_inv_lref2_lt … Hi ?) -Hi /2 width=3/ /3 width=3/
 | #i #d1 #e1 #Hid1 #d2 #e2 #T2 #Hi #Hd12
-  elim (lift_inv_lref2 … Hi) -Hi * #Hid2 #H destruct -T2
-  [ -Hd12; lapply (lt_plus_to_lt_l … Hid2) -Hid2 #Hid2 /3/
-  | -Hid1; lapply (arith1 … Hid2) -Hid2 #Hid2
+  elim (lift_inv_lref2 … Hi) -Hi * #Hid2 #H destruct
+  [ -Hd12 lapply (lt_plus_to_lt_l … Hid2) -Hid2 #Hid2 /3 width=3/
+  | -Hid1 lapply (arith1 … Hid2) -Hid2 #Hid2
     @(ex2_1_intro … #(i - e2))
-    [ >le_plus_minus_comm [ @lift_lref_ge @(transitive_le … Hd12) -Hd12 /2/ | -Hd12 /2/ ]
-    | -Hd12 >(plus_minus_m_m i e2) in ⊢ (? ? ? ? %) /2/ /3/
+    [ >le_plus_minus_comm [ @lift_lref_ge @(transitive_le … Hd12) -Hd12 /2 width=1/ | -Hd12 /2 width=2/ ]
+    | -Hd12 >(plus_minus_m_m i e2) in ⊢ (? ? ? ? %); /2 width=2/ /3 width=1/
     ]
   ]
 | #p #d1 #e1 #d2 #e2 #T2 #Hk #Hd12
-  lapply (lift_inv_gref2 … Hk) -Hk #Hk destruct -T2 /3/
+  lapply (lift_inv_gref2 … Hk) -Hk #Hk destruct /3 width=3/
 | #I #W1 #W #U1 #U #d1 #e1 #_ #_ #IHW #IHU #d2 #e2 #T2 #H #Hd12
-  lapply (lift_inv_bind2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct -T2;
-  elim (IHW … HW2 ?) // -IHW HW2 #W0 #HW2 #HW1
-  >plus_plus_comm_23 in HU2 #HU2 elim (IHU … HU2 ?) /2/ /3 width = 5/
+  lapply (lift_inv_bind2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct
+  elim (IHW … HW2 ?) // -IHW -HW2 #W0 #HW2 #HW1
+  >plus_plus_comm_23 in HU2; #HU2 elim (IHU … HU2 ?) /2 width=1/ /3 width=5/
 | #I #W1 #W #U1 #U #d1 #e1 #_ #_ #IHW #IHU #d2 #e2 #T2 #H #Hd12
-  lapply (lift_inv_flat2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct -T2;
-  elim (IHW … HW2 ?) // -IHW HW2 #W0 #HW2 #HW1
-  elim (IHU … HU2 ?) // /3 width = 5/
+  lapply (lift_inv_flat2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct
+  elim (IHW … HW2 ?) // -IHW -HW2 #W0 #HW2 #HW1
+  elim (IHU … HU2 ?) // /3 width=5/
 ]
 qed.
 
 theorem lift_mono: ∀d,e,T,U1. ↑[d,e] T ≡ U1 → ∀U2. ↑[d,e] T ≡ U2 → U1 = U2.
-#d #e #T #U1 #H elim H -H d e T U1
+#d #e #T #U1 #H elim H -d -e -T -U1
 [ #k #d #e #X #HX
   lapply (lift_inv_sort1 … HX) -HX //
 | #i #d #e #Hid #X #HX 
@@ -80,9 +80,9 @@ theorem lift_mono: ∀d,e,T,U1. ↑[d,e] T ≡ U1 → ∀U2. ↑[d,e] T ≡ U2 
 | #p #d #e #X #HX
   lapply (lift_inv_gref1 … HX) -HX //
 | #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_bind1 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/
+  elim (lift_inv_bind1 … HX) -HX #V #T #HV1 #HT1 #HX destruct /3 width=1/
 | #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_flat1 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/
+  elim (lift_inv_flat1 … HX) -HX #V #T #HV1 #HT1 #HX destruct /3 width=1/
 ]
 qed-.
 
@@ -90,27 +90,27 @@ qed-.
 theorem lift_trans_be: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
                        ∀d2,e2,T2. ↑[d2, e2] T ≡ T2 →
                        d1 ≤ d2 → d2 ≤ d1 + e1 → ↑[d1, e1 + e2] T1 ≡ T2.
-#d1 #e1 #T1 #T #H elim H -H d1 e1 T1 T
+#d1 #e1 #T1 #T #H elim H -d1 -e1 -T1 -T
 [ #k #d1 #e1 #d2 #e2 #T2 #HT2 #_ #_
   >(lift_inv_sort1 … HT2) -HT2 //
 | #i #d1 #e1 #Hid1 #d2 #e2 #T2 #HT2 #Hd12 #_
   lapply (lt_to_le_to_lt … Hid1 Hd12) -Hd12 #Hid2
-  lapply (lift_inv_lref1_lt … HT2 Hid2) /2/
+  lapply (lift_inv_lref1_lt … HT2 Hid2) /2 width=1/
 | #i #d1 #e1 #Hid1 #d2 #e2 #T2 #HT2 #_ #Hd21
   lapply (lift_inv_lref1_ge … HT2 ?) -HT2
-  [ @(transitive_le … Hd21 ?) -Hd21 /2/
-  | -Hd21 /2/
+  [ @(transitive_le … Hd21 ?) -Hd21 /2 width=1/
+  | -Hd21 /2 width=1/
   ]
 | #p #d1 #e1 #d2 #e2 #T2 #HT2 #_ #_
   >(lift_inv_gref1 … HT2) -HT2 //
 | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd12 #Hd21
-  elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X;
-  lapply (IHV12 … HV20 ? ?) // -IHV12 HV20 #HV10
-  lapply (IHT12 … HT20 ? ?) /2/
+  elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct
+  lapply (IHV12 … HV20 ? ?) // -IHV12 -HV20 #HV10
+  lapply (IHT12 … HT20 ? ?) /2 width=1/
 | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd12 #Hd21
-  elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X;
-  lapply (IHV12 … HV20 ? ?) // -IHV12 HV20 #HV10
-  lapply (IHT12 … HT20 ? ?) // /2/
+  elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct
+  lapply (IHV12 … HV20 ? ?) // -IHV12 -HV20 #HV10
+  lapply (IHT12 … HT20 ? ?) // /2 width=1/
 ]
 qed.
 
@@ -118,26 +118,26 @@ qed.
 theorem lift_trans_le: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
                        ∀d2,e2,T2. ↑[d2, e2] T ≡ T2 → d2 ≤ d1 →
                        ∃∃T0. ↑[d2, e2] T1 ≡ T0 & ↑[d1 + e2, e1] T0 ≡ T2.
-#d1 #e1 #T1 #T #H elim H -H d1 e1 T1 T
+#d1 #e1 #T1 #T #H elim H -d1 -e1 -T1 -T
 [ #k #d1 #e1 #d2 #e2 #X #HX #_
-  >(lift_inv_sort1 … HX) -HX /2/
+  >(lift_inv_sort1 … HX) -HX /2 width=3/
 | #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #_
   lapply (lt_to_le_to_lt … (d1+e2) Hid1 ?) // #Hie2
-  elim (lift_inv_lref1 … HX) -HX * #Hid2 #HX destruct -X /3/ /4/
+  elim (lift_inv_lref1 … HX) -HX * #Hid2 #HX destruct /3 width=3/ /4 width=3/
 | #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #Hd21
   lapply (transitive_le … Hd21 Hid1) -Hd21 #Hid2
-  lapply (lift_inv_lref1_ge … HX ?) -HX /2/ #HX destruct -X;
-  >plus_plus_comm_23 /4/
+  lapply (lift_inv_lref1_ge … HX ?) -HX /2 width=1/ #HX destruct
+  >plus_plus_comm_23 /4 width=3/
 | #p #d1 #e1 #d2 #e2 #X #HX #_
-  >(lift_inv_gref1 … HX) -HX /2/
+  >(lift_inv_gref1 … HX) -HX /2 width=3/
 | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd21
-  elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X;
-  elim (IHV12 … HV20 ?) -IHV12 HV20 //
-  elim (IHT12 … HT20 ?) -IHT12 HT20 /2/ /3 width=5/
+  elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct
+  elim (IHV12 … HV20 ?) -IHV12 -HV20 //
+  elim (IHT12 … HT20 ?) -IHT12 -HT20 /2 width=1/ /3 width=5/
 | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd21
-  elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X;
-  elim (IHV12 … HV20 ?) -IHV12 HV20 //
-  elim (IHT12 … HT20 ?) -IHT12 HT20 // /3 width=5/
+  elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct
+  elim (IHV12 … HV20 ?) -IHV12 -HV20 //
+  elim (IHT12 … HT20 ?) -IHT12 -HT20 // /3 width=5/
 ]
 qed.
 
@@ -145,27 +145,27 @@ qed.
 theorem lift_trans_ge: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
                        ∀d2,e2,T2. ↑[d2, e2] T ≡ T2 → d1 + e1 ≤ d2 →
                        ∃∃T0. ↑[d2 - e1, e2] T1 ≡ T0 & ↑[d1, e1] T0 ≡ T2.
-#d1 #e1 #T1 #T #H elim H -H d1 e1 T1 T
+#d1 #e1 #T1 #T #H elim H -d1 -e1 -T1 -T
 [ #k #d1 #e1 #d2 #e2 #X #HX #_
-  >(lift_inv_sort1 … HX) -HX /2/
+  >(lift_inv_sort1 … HX) -HX /2 width=3/
 | #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #Hded
   lapply (lt_to_le_to_lt … (d1+e1) Hid1 ?) // #Hid1e
-  lapply (lt_to_le_to_lt … (d2-e1) Hid1 ?) /2/ #Hid2e
-  lapply (lt_to_le_to_lt … Hid1e Hded) -Hid1e Hded #Hid2
-  lapply (lift_inv_lref1_lt … HX ?) -HX // #HX destruct -X /3/
+  lapply (lt_to_le_to_lt … (d2-e1) Hid1 ?) /2 width=1/ #Hid2e
+  lapply (lt_to_le_to_lt … Hid1e Hded) -Hid1e -Hded #Hid2
+  lapply (lift_inv_lref1_lt … HX ?) -HX // #HX destruct /3 width=3/
 | #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #_
-  elim (lift_inv_lref1 … HX) -HX * #Hied #HX destruct -X;
-  [ /4/ | >plus_plus_comm_23 /4/ ]
+  elim (lift_inv_lref1 … HX) -HX * #Hied #HX destruct
+  [ /4 width=3/ | >plus_plus_comm_23 /4 width=3/ ]
 | #p #d1 #e1 #d2 #e2 #X #HX #_
-  >(lift_inv_gref1 … HX) -HX /2/
+  >(lift_inv_gref1 … HX) -HX /2 width=3/
 | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hded
-  elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X;
-  elim (IHV12 … HV20 ?) -IHV12 HV20 //
-  elim (IHT12 … HT20 ?) -IHT12 HT20 /2/ #T
-  <plus_minus /2/ /3 width=5/
+  elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct
+  elim (IHV12 … HV20 ?) -IHV12 -HV20 //
+  elim (IHT12 … HT20 ?) -IHT12 -HT20 /2 width=1/ #T
+  <plus_minus /2 width=2/ /3 width=5/
 | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hded
-  elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X;
-  elim (IHV12 … HV20 ?) -IHV12 HV20 //
-  elim (IHT12 … HT20 ?) -IHT12 HT20 // /3 width=5/
+  elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct
+  elim (IHV12 … HV20 ?) -IHV12 -HV20 //
+  elim (IHT12 … HT20 ?) -IHT12 -HT20 // /3 width=5/
 ]
 qed.