bug fix in supclosure allows alternative definition of fpbs !

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cpxs_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
index 25544dd41d2f6de45f4bbf9e8215b0a52d92ee18..182043d3b5d4f704d8d254aeccbc9604cb4b9eac 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
@@ -26,17 +26,20 @@ lemma lsstas_cpxs: ∀h,g,G,L,T1,T2,l1. ⦃G, L⦄ ⊢ T1 •* [h, g, l1] T2 →
 #h #g #G #L #T1 #T2 #l1 #H @(lsstas_ind_dx … H) -T2 -l1 //
 #l1 #T #T2 #HT1 #HT2 #IHT1 #l2 #Hl2 #Hl12
 lapply (lsstas_da_conf … HT1 … Hl2) -HT1
->(plus_minus_m_m (l2-l1) 1 ?) [2: /2 width=1/ ]
-/4 width=5 by cpxs_strap1, ssta_cpx, lt_to_le/
+>(plus_minus_m_m (l2-l1) 1 ?)
+[ /4 width=5 by cpxs_strap1, ssta_cpx, lt_to_le/
+| /2 width=1 by monotonic_le_minus_r/
+]
 qed.
 
 lemma cpxs_delta: ∀h,g,I,G,L,K,V,V2,i.
                   ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ➡*[h, g] V2 →
                   ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡*[h, g] W2.
-#h #g #I #G #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=9/ ]
-#V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2
-lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK
-elim (lift_total V1 0 (i+1)) /4 width=11 by cpx_lift, cpxs_strap1/
+#h #g #I #G #L #K #V #V2 #i #HLK #H elim H -V2
+[ /3 width=9 by cpx_cpxs, cpx_delta/
+| #V1 lapply (ldrop_fwd_ldrop2 … HLK) -HLK
+  elim (lift_total V1 0 (i+1)) /4 width=11 by cpx_lift, cpxs_strap1/
+]
 qed.
 
 (* Advanced inversion lemmas ************************************************)
@@ -45,21 +48,22 @@ lemma cpxs_inv_lref1: ∀h,g,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡*[h, g] T2 →
                       T2 = #i ∨
                       ∃∃I,K,V1,T1. ⇩[0, i] L ≡ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ➡*[h, g] T1 &
                                    ⇧[0, i + 1] T1 ≡ T2.
-#h #g #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1/
+#h #g #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct
-  elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1/
-  * /4 width=7/
+  elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
+  * /4 width=7 by cpx_cpxs, ex3_4_intro, or_intror/
 | * #I #K #V1 #T1 #HLK #HVT1 #HT1
   lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
-  elim (cpx_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T /4 width=7/
+  elim (cpx_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T
+  /4 width=7 by cpxs_strap1, ex3_4_intro, or_intror/
 ]
 qed-.
 
 (* Relocation properties ****************************************************)
 
 lemma cpxs_lift: ∀h,g,G. l_liftable (cpxs h g G).
-/3 width=9/ qed.
+/3 width=9 by cpx_lift, cpxs_strap1, l_liftable_LTC/ qed.
 
 lemma cpxs_inv_lift1: ∀h,g,G. l_deliftable_sn (cpxs h g G).
 /3 width=5 by l_deliftable_sn_LTC, cpx_inv_lift1/
@@ -70,10 +74,12 @@ qed-.
 lemma fsupq_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
                         ∀T1. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
                         ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 [ /3 width=3/ ]
-#T #T2 #HT2 #_ #IHTU2 #T1 #HT1
-elim (fsupq_cpx_trans … HT1 … HT2) -T #T #HT1 #HT2
-elim (IHTU2 … HT2) -T2 /3 width=3/
+#h #g #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2
+[ /3 width=3 by fsupq_fsups, ex2_intro/
+| #T #T2 #HT2 #_ #IHTU2 #T1 #HT1
+  elim (fsupq_cpx_trans … HT1 … HT2) -T #T #HT1 #HT2
+  elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
+]
 qed-.
 
 lemma fsupq_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
@@ -85,11 +91,12 @@ lemma fsupq_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G
 lemma fsups_cpxs_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
                         ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsups_ind … H) -G2 -L2 -T2 [ /2 width=3/ ]
-#G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2
-elim (fsupq_cpxs_trans … HTU2 … HT2) -T2 #T2 #HT2 #HTU2
-elim (IHT1 … HT2) -T #T #HT1 #HT2
-lapply (fsups_trans … HT2 … HTU2) -G -L -T2 /2 width=3/
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsups_ind … H) -G2 -L2 -T2
+[ /2 width=3 by ex2_intro/
+| #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2
+  elim (fsupq_cpxs_trans … HTU2 … HT2) -T2 #T2 #HT2 #HTU2
+  elim (IHT1 … HT2) -T /3 width=7 by fsups_trans, ex2_intro/
+]
 qed-.
 
 lemma fsups_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
@@ -97,3 +104,14 @@ lemma fsups_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2,
                           ∀l2. ⦃G2, L2⦄ ⊢ T2 ▪ [h, g] l2 → l1 ≤ l2 →
                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
 /3 width=7 by fsups_cpxs_trans, lsstas_cpxs/ qed-.
+
+lemma fsups_cpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
+                       ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 →
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsups_ind … H) -G2 -L2 -T2
+[ /2 width=3 by ex2_intro/
+| #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2
+  elim (fsupq_cpx_trans … HT2 … HTU2) -T2 #T2 #HT2 #HTU2
+  elim (IHT1 … HT2) -T /3 width=7 by fsups_strap1, ex2_intro/
+]
+qed-.
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