- partial commit of rt_transition ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_new / lstas / lstas_lift.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_new/lstas/lstas_lift.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_new/lstas/lstas_lift.etc
index 97cf7e7db6195f2bc1cd8486c844c75140366adf..225b6d78142e078ead162340719869566f584b9f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_new/lstas/lstas_lift.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_new/lstas/lstas_lift.etc
@@ -23,10 +23,10 @@ include "basic_2/unfold/lstas.ma".
 (* Basic_1: was just: sty0_lift *)
 lemma lstas_lift: ∀h,G,d. d_liftable (lstas h G d).
 #h #G #d #L1 #T1 #U1 #H elim H -G -L1 -T1 -U1 -d
-[ #G #L1 #d #k #L2 #s #l #m #HL21 #X1 #H1 #X2 #H2
+[ #G #L1 #d #s #L2 #c #l #k #HL21 #X1 #H1 #X2 #H2
   >(lift_inv_sort1 … H1) -X1
   >(lift_inv_sort1 … H2) -X2 //
-| #G #L1 #K1 #V1 #W1 #W #i #d #HLK1 #_ #HW1 #IHVW1 #L2 #s #l #m #HL21 #X #H #U2 #HWU2
+| #G #L1 #K1 #V1 #W1 #W #i #d #HLK1 #_ #HW1 #IHVW1 #L2 #c #l #k #HL21 #X #H #U2 #HWU2
   elim (lift_inv_lref1 … H) * #Hil #H destruct
   [ elim (lift_trans_ge … HW1 … HWU2) -W /2 width=1 by ylt_fwd_le_succ1/ #W2 #HW12 #HWU2
     elim (drop_trans_le … HL21 … HLK1) -L1 /2 width=2 by ylt_fwd_le/ #X #HLK2 #H
@@ -35,17 +35,17 @@ lemma lstas_lift: ∀h,G,d. d_liftable (lstas h G d).
   | lapply (lift_trans_be … HW1 … HWU2 ? ?) -W /2 width=1 by yle_succ_dx/ #HW1U2
     lapply (drop_trans_ge … HL21 … HLK1 ?) -L1 /3 width=9 by lstas_ldef, drop_inv_gen/
   ]
-| #G #L1 #K1 #V1 #W1 #i #HLK1 #_ #IHVW1 #L2 #s #l #m #HL21 #X #H #U2 #HWU2
+| #G #L1 #K1 #V1 #W1 #i #HLK1 #_ #IHVW1 #L2 #c #l #k #HL21 #X #H #U2 #HWU2
   >(lift_mono … HWU2 … H) -U2
   elim (lift_inv_lref1 … H) * #Hil #H destruct
-  [ elim (lift_total W1 (l-i-1) m) #W2 #HW12
+  [ elim (lift_total W1 (l-i-1) k) #W2 #HW12
     elim (drop_trans_le … HL21 … HLK1) -L1 /2 width=2 by ylt_fwd_le/ #X #HLK2 #H
     elim (drop_inv_skip2 … H) -H /2 width=1 by ylt_to_minus/ -Hil #K2 #V2 #HK21 #HV12 #H destruct
     /3 width=10 by lstas_zero/
   | lapply (drop_trans_ge … HL21 … HLK1 ?) -L1
     /3 width=10 by lstas_zero, drop_inv_gen/
   ]
-| #G #L1 #K1 #W1 #V1 #W #i #d #HLK1 #_ #HW1 #IHWV1 #L2 #s #l #m #HL21 #X #H #U2 #HWU2
+| #G #L1 #K1 #W1 #V1 #W #i #d #HLK1 #_ #HW1 #IHWV1 #L2 #c #l #k #HL21 #X #H #U2 #HWU2
   elim (lift_inv_lref1 … H) * #Hil #H destruct
   [ elim (lift_trans_ge … HW1 … HWU2) -W /2 width=1 by ylt_fwd_le_succ1/ #W #HW1 #HWU2
     elim (drop_trans_le … HL21 … HLK1) -L1 /2 width=2 by ylt_fwd_le/ #X #HLK2 #H
@@ -54,15 +54,15 @@ lemma lstas_lift: ∀h,G,d. d_liftable (lstas h G d).
   | lapply (lift_trans_be … HW1 … HWU2 ? ?) -W /2 width=1 by yle_succ_dx/ #HW1U2
     lapply (drop_trans_ge … HL21 … HLK1 ?) -L1 /3 width=9 by lstas_succ, drop_inv_gen/
   ]
-| #a #I #G #L1 #V1 #T1 #U1 #d #_ #IHTU1 #L2 #s #l #m #HL21 #X1 #H1 #X2 #H2
+| #a #I #G #L1 #V1 #T1 #U1 #d #_ #IHTU1 #L2 #c #l #k #HL21 #X1 #H1 #X2 #H2
   elim (lift_inv_bind1 … H1) -H1 #V2 #T2 #HV12 #HT12 #H destruct
   elim (lift_inv_bind1 … H2) -H2 #X #U2 #H1 #HU12 #H2 destruct
   lapply (lift_mono … H1 … HV12) -H1 #H destruct /4 width=6 by lstas_bind, drop_skip/
-| #G #L1 #V1 #T1 #U1 #d #_ #IHTU1 #L2 #s #l #m #HL21 #X1 #H1 #X2 #H2
+| #G #L1 #V1 #T1 #U1 #d #_ #IHTU1 #L2 #c #l #k #HL21 #X1 #H1 #X2 #H2
   elim (lift_inv_flat1 … H1) -H1 #V2 #T2 #HV12 #HT12 #H destruct
   elim (lift_inv_flat1 … H2) -H2 #X #U2 #H1 #HU12 #H2 destruct
   lapply (lift_mono … H1 … HV12) -H1 #H destruct /4 width=6 by lstas_appl/
-| #G #L1 #W1 #T1 #U1 #d #_ #IHTU1 #L2 #s #l #m #HL21 #X #H #U2 #HU12
+| #G #L1 #W1 #T1 #U1 #d #_ #IHTU1 #L2 #c #l #k #HL21 #X #H #U2 #HU12
   elim (lift_inv_flat1 … H) -H #W2 #T2 #_ #HT12 #H destruct /3 width=6 by lstas_cast/
 ]
 qed.
@@ -72,19 +72,19 @@ qed.
 (* Note: apparently this was missing in basic_1 *)
 lemma lstas_inv_lift1: ∀h,G,d. d_deliftable_sn (lstas h G d).
 #h #G #d #L2 #T2 #U2 #H elim H -G -L2 -T2 -U2 -d
-[ #G #L2 #d #k #L1 #s #l #m #_ #X #H
+[ #G #L2 #d #s #L1 #c #l #k #_ #X #H
   >(lift_inv_sort2 … H) -X /2 width=3 by lstas_sort, lift_sort, ex2_intro/
-| #G #L2 #K2 #V2 #W2 #W #i #d #HLK2 #HVW2 #HW2 #IHVW2 #L1 #s #l #m #HL21 #X #H
+| #G #L2 #K2 #V2 #W2 #W #i #d #HLK2 #HVW2 #HW2 #IHVW2 #L1 #c #l #k #HL21 #X #H
   elim (lift_inv_lref2 … H) * #Hil #H destruct [ -HVW2 | -IHVW2 ]
   [ elim (drop_conf_lt … HL21 … HLK2) -L2 // #K1 #V1 #HLK1 #HK21 #HV12
     elim (IHVW2 … HK21 … HV12) -K2 -V2 #W1 #HW12 #HVW1
     elim (lift_trans_le … HW12 … HW2) -W2 // <yminus_succ2 <yplus_inj >yplus_SO2 >ymax_pre_sn /3 width=8 by lstas_ldef, ylt_fwd_le_succ1, ex2_intro/
   | lapply (drop_conf_ge … HL21 … HLK2 ?) -L2 // #HL1K2
     elim (yle_inv_plus_inj2 … Hil) -Hil #Hlim #mi
-    elim (lift_split … HW2 l (i-m+1)) -HW2 /2 width=1 by yle_succ_dx, le_S_S/
-    #W0 #HW20 <le_plus_minus_comm /2 width=1 by yle_inv_inj/ >minus_minus_m_m /3 width=8 by lstas_ldef, yle_inv_inj, le_S, ex2_intro/
+    elim (lift_split … HW2 l (i-k+1)) -HW2 /2 width=1 by yle_succ_dx, le_S_S/
+    #W0 #HW20 <le_plus_minus_comm /2 width=1 by yle_inv_inj/ >minus_minus_k_k /3 width=8 by lstas_ldef, yle_inv_inj, le_S, ex2_intro/
   ]
-| #G #L2 #K2 #W2 #V2 #i #HLK2 #HWV2 #IHWV2 #L1 #s #l #m #HL21 #X #H
+| #G #L2 #K2 #W2 #V2 #i #HLK2 #HWV2 #IHWV2 #L1 #c #l #k #HL21 #X #H
   elim (lift_inv_lref2 … H) * #Hil #H destruct [ -HWV2 | -IHWV2 ]
   [ elim (drop_conf_lt … HL21 … HLK2) -L2 // #K1 #W1 #HLK1 #HK21 #HW12
     elim (IHWV2 … HK21 … HW12) -K2
@@ -92,23 +92,23 @@ lemma lstas_inv_lift1: ∀h,G,d. d_deliftable_sn (lstas h G d).
   | lapply (drop_conf_ge … HL21 … HLK2 ?) -L2
     /3 width=5 by lstas_zero, lift_lref_ge_minus, ex2_intro/
   ]
-| #G #L2 #K2 #W2 #V2 #W #i #d #HLK2 #HWV2 #HW2 #IHWV2 #L1 #s #l #m #HL21 #X #H
+| #G #L2 #K2 #W2 #V2 #W #i #d #HLK2 #HWV2 #HW2 #IHWV2 #L1 #c #l #k #HL21 #X #H
   elim (lift_inv_lref2 … H) * #Hil #H destruct [ -HWV2 | -IHWV2 ]
   [ elim (drop_conf_lt … HL21 … HLK2) -L2 // #K1 #W1 #HLK1 #HK21 #HW12
     elim (IHWV2 … HK21 … HW12) -K2 #V1 #HV12 #HWV1
     elim (lift_trans_le … HV12 … HW2) -W2 // <yminus_succ2 <yplus_inj >yplus_SO2 >ymax_pre_sn /3 width=8 by lstas_succ, ylt_fwd_le_succ1, ex2_intro/
   | lapply (drop_conf_ge … HL21 … HLK2 ?) -L2 // #HL1K2
     elim (yle_inv_plus_inj2  … Hil) -Hil #Hlim #mi
-    elim (lift_split … HW2 l (i-m+1)) -HW2 /2 width=1 by yle_succ_dx, le_S_S/
-    #W0 #HW20 <le_plus_minus_comm /2 width=1 by yle_inv_inj/ >minus_minus_m_m /3 width=8 by lstas_succ, yle_inv_inj, le_S, ex2_intro/
+    elim (lift_split … HW2 l (i-k+1)) -HW2 /2 width=1 by yle_succ_dx, le_S_S/
+    #W0 #HW20 <le_plus_minus_comm /2 width=1 by yle_inv_inj/ >minus_minus_k_k /3 width=8 by lstas_succ, yle_inv_inj, le_S, ex2_intro/
   ]
-| #a #I #G #L2 #V2 #T2 #U2 #d #_ #IHTU2 #L1 #s #l #m #HL21 #X #H
+| #a #I #G #L2 #V2 #T2 #U2 #d #_ #IHTU2 #L1 #c #l #k #HL21 #X #H
   elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
   elim (IHTU2 (L1.ⓑ{I}V1) … HT12) -IHTU2 -HT12 /3 width=5 by lstas_bind, drop_skip, lift_bind, ex2_intro/
-| #G #L2 #V2 #T2 #U2 #d #_ #IHTU2 #L1 #s #l #m #HL21 #X #H
+| #G #L2 #V2 #T2 #U2 #d #_ #IHTU2 #L1 #c #l #k #HL21 #X #H
   elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
   elim (IHTU2 … HL21 … HT12) -L2 -HT12 /3 width=5 by lstas_appl, lift_flat, ex2_intro/
-| #G #L2 #W2 #T2 #U2 #d #_ #IHTU2 #L1 #s #l #m #HL21 #X #H
+| #G #L2 #W2 #T2 #U2 #d #_ #IHTU2 #L1 #c #l #k #HL21 #X #H
   elim (lift_inv_flat2 … H) -H #W1 #T1 #_ #HT12 #H destruct
   elim (IHTU2 … HL21 … HT12) -L2 -HT12 /3 width=3 by lstas_cast, ex2_intro/
 ]
@@ -119,7 +119,7 @@ qed-.
 lemma lstas_split_aux: ∀h,G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 •*[h, d] T2 → ∀d1,d2. d = d1 + d2 →
                        ∃∃T. ⦃G, L⦄ ⊢ T1 •*[h, d1] T & ⦃G, L⦄ ⊢ T •*[h, d2] T2.
 #h #G #L #T1 #T2 #d #H elim H -G -L -T1 -T2 -d
-[ #G #L #d #k #d1 #d2 #H destruct
+[ #G #L #d #s #d1 #d2 #H destruct
   >commutative_plus >iter_plus /2 width=3 by lstas_sort, ex2_intro/
 | #G #L #K #V1 #V2 #U2 #i #d #HLK #_ #VU2 #IHV12 #d1 #d2 #H destruct
   elim (IHV12 d1 d2) -IHV12 // #V