- degree assignment, static type assignment, iterated static type

[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 52aff988f9a5849376404d3da6654babfa0d05d2..25544dd41d2f6de45f4bbf9e8215b0a52d92ee18 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
@@ -12,6 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/substitution/fsups_fsups.ma".
+include "basic_2/unfold/lsstas_lift.ma".
 include "basic_2/reduction/cpx_lift.ma".
 include "basic_2/computation/cpxs.ma".
 
@@ -19,10 +21,19 @@ include "basic_2/computation/cpxs.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma cpxs_delta: ∀h,g,I,L,K,V,V2,i.
-                  ⇩[0, i] L ≡ K. ⓑ{I}V → ⦃h, K⦄ ⊢ V ➡*[g] V2 →
-                  ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃h, L⦄ ⊢ #i ➡*[g] W2.
-#h #g #I #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=9/ ]
+lemma lsstas_cpxs: ∀h,g,G,L,T1,T2,l1. ⦃G, L⦄ ⊢ T1 •* [h, g, l1] T2 →
+                   ∀l2. ⦃G, L⦄ ⊢ T1 ▪ [h, g] l2 → l1 ≤ l2 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] 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/
+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/
@@ -30,11 +41,11 @@ qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpxs_inv_lref1: ∀h,g,L,T2,i. ⦃h, L⦄ ⊢ #i ➡*[g] T2 →
+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 & ⦃h, K⦄ ⊢ V1 ➡*[g] T1 &
+                      ∃∃I,K,V1,T1. ⇩[0, i] L ≡ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ➡*[h, g] T1 &
                                    ⇧[0, i + 1] T1 ≡ T2.
-#h #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/
 #T #T2 #_ #HT2 *
 [ #H destruct
   elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1/
@@ -47,29 +58,42 @@ qed-.
 
 (* Relocation properties ****************************************************)
 
-(* Basic_1: was: pr3_lift *)
-lemma cpxs_lift: ∀h,g. l_liftable (cpxs h g).
+lemma cpxs_lift: ∀h,g,G. l_liftable (cpxs h g G).
 /3 width=9/ qed.
 
-(* Basic_1: was: pr3_gen_lift *)
-lemma cpxs_inv_lift1: ∀h,g. l_deliftable_sn (cpxs h g).
+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/
 qed-.
 
 (* Properties on supclosure *************************************************)
 
-include "basic_2/substitution/fsups.ma".
-
-lemma fsupq_cpxs_trans: ∀h,g,L1,L2,T2,U2. ⦃h, L2⦄ ⊢ T2 ➡*[g] U2 →
-                        ∀T1. ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄ →
-                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡*[g] U1 & ⦃L1, U1⦄ ⊃* ⦃L2, U2⦄.
-#h #g #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 [ /3 width=3/ ]
+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/
 qed-.
 
-lemma fsup_ssta_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
-                       ∀U2,l. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l+1, U2⦄ →
-                       ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃⸮ ⦃L2, U2⦄.
-/3 width=4 by fsup_cpx_trans, ssta_cpx/ qed-.
+lemma fsupq_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
+                          ∀U2,l1. ⦃G2, L2⦄ ⊢ T2 •*[h, g, l1] U2 →
+                          ∀l2. ⦃G2, L2⦄ ⊢ T2 ▪ [h, g] l2 → l1 ≤ l2 →
+                          ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
+/3 width=5 by fsupq_cpxs_trans, lsstas_cpxs/ qed-.
+
+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/
+qed-.
+
+lemma fsups_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
+                          ∀U2,l1. ⦃G2, L2⦄ ⊢ T2 •*[h, g, l1] U2 →
+                          ∀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-.