milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / sta / da_sta.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/sta/da_sta.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/sta/da_sta.etc
deleted file mode 100644 (file)
index 4f45a81..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/sta/da_sta.etc
+++ /dev/null
@@ -1,86 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/static/sta.ma".
-include "basic_2/static/da_da.ma".
-
-(* Properties on static type assignment for terms ***************************)
-
-lemma da_sta_conf: ∀h,g,G,L,T,U. ⦃G, L⦄ ⊢ T •[h] U →
-                   ∀l. ⦃G, L⦄ ⊢ T ▪[h, g] l → ⦃G, L⦄ ⊢ U ▪[h, g] l-1.
-#h #g #G #L #T #U #H elim H -G -L -T -U
-[ #G #L #k #l #H
-  lapply (da_inv_sort … H) -H /3 width=1 by da_sort, deg_next/
-| #G #L #K #V #U #W #i #HLK #_ #HWU #IHVW #l #H
-  elim (da_inv_lref … H) -H * #K0 #V0 [| #l0] #HLK0 #HV0
-  lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct
-  lapply (drop_fwd_drop2 … HLK) -HLK /3 width=8 by da_lift/
-| #G #L #K #W #V #U #i #HLK #_ #HWU #IHWV #l #H
-  elim (da_inv_lref … H) -H * #K0 #V0 [| #l0] #HLK0 #HV0 [| #H0 ]
-  lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct
-  lapply (drop_fwd_drop2 … HLK) -HLK /3 width=8 by da_lift/
-| #a #I #G #L #V #T #U #_ #IHTU #l #H
-  lapply (da_inv_bind … H) -H /3 width=1 by da_bind/
-| #G #L #V #T #U #_ #IHTU #l #H
-  lapply (da_inv_flat … H) -H /3 width=1 by da_flat/
-| #G #L #W #T #U #_ #IHTU #l #H
-  lapply (da_inv_flat … H) -H /2 width=1 by/
-]
-qed-.
-
-lemma sta_da: ∀h,g,G,L,T,U. ⦃G, L⦄ ⊢ T •[h] U →
-              ∃l. ⦃G, L⦄ ⊢ T ▪[h, g] l.
-#h #g #G #L #T #U #H elim H -G -L -T -U
-[ #G #L #k elim (deg_total h g k) /3 width=2 by da_sort, ex_intro/
-| #G #L #K #V #W #W0 #i #HLK #_ #_ * /3 width=5 by da_ldef, ex_intro/
-| #G #L #K #W #V #W0 #i #HLK #_ #_ * /3 width=5 by da_ldec, ex_intro/
-| #a #I #G #L #V #T #U #_ * /3 width=2 by da_bind, ex_intro/
-| #G #L #V #T #U #_ * /3 width=2 by da_flat, ex_intro/
-| #G #L #W #T #U #_ * /3 width=2 by da_flat, ex_intro/
-]
-qed-.
-
-lemma sta_da_ge: ∀h,G,L,T,U,l0. ⦃G, L⦄ ⊢ T •[h] U →
-                 ∃∃g,l. ⦃G, L⦄ ⊢ T ▪[h, g] l & l0 ≤ l.
-#h #G #L #T #U #l0 #H elim H -G -L -T -U
-[ /3 width=4 by da_sort, ex2_2_intro/
-| #G #L #K #V #W #W0 #i #HLK #_ #_ * /3 width=5 by da_ldef, ex2_2_intro/
-| #G #L #K #W #V #W0 #i #HLK #_ #_ * /4 width=5 by da_ldec, lt_to_le, le_S_S, ex2_2_intro/
-| #a #I #G #L #V #T #U #_ * /3 width=4 by da_bind, ex2_2_intro/
-| #G #L #V #T #U #_ * /3 width=4 by da_flat, ex2_2_intro/
-| #G #L #W #T #U #_ * /3 width=4 by da_flat, ex2_2_intro/
-]
-qed-.
-
-(* Inversion lrmmas on static type assignment for terms *********************)
-
-lemma da_inv_sta: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l →
-                  ∃U. ⦃G, L⦄ ⊢ T •[h] U.
-#h #g #G #L #T #l #H elim H -G -L -T -l
-[ /2 width=2/
-| #G #L #K #V #i #l #HLK #_ * #W #HVW
-  elim (lift_total W 0 (i+1)) /3 width=7 by sta_ldef, ex_intro/
-| #G #L #K #W #i #l #HLK #_ * #V #HWV
-  elim (lift_total W 0 (i+1)) /3 width=7 by sta_ldec, ex_intro/
-| #a #I #G #L #V #T #l #_ * /3 width=2 by sta_bind, ex_intro/
-| * #G #L #V #T #l #_ * /3 width=2 by sta_appl, sta_cast, ex_intro/
-]
-qed-.
-
-lemma sta_inv_refl_pos: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h] T → ⊥.
-#h #g #G #L #T #l #H1T #HTT
-lapply (da_sta_conf … HTT … H1T) -HTT <minus_plus_m_m #H2T
-lapply (da_mono … H2T … H1T) -h -G -L -T #H
-elim (plus_xySz_x_false 0 l 0) //
-qed-.