X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc_2A1%2Fnta%2Fnta_lift.etc;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc_2A1%2Fnta%2Fnta_lift.etc;h=0000000000000000000000000000000000000000;hb=5c92c318030a05c766b3f6070dbd23589cbdee04;hp=57e06a1e9aaff1c1c38a2900686ca414d8e18069;hpb=e9b09b14538f770b9e65083c24e3e9cf487df648;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/nta/nta_lift.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/nta/nta_lift.etc deleted file mode 100644 index 57e06a1e9..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/nta/nta_lift.etc +++ /dev/null @@ -1,144 +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/dynamic/nta_alt.ma". - -(* NATIVE TYPE ASSIGNMENT ON TERMS ******************************************) - -(* Advanced inversion lemmas ************************************************) - -fact nta_inv_sort1_aux: ∀h,L,T,U. ⦃h, L⦄ ⊢ T : U → ∀k0. T = ⋆k0 → - L ⊢ ⋆(next h k0) ⬌* U. -#h #L #T #U #H elim H -L -T -U -[ #L #k #k0 #H destruct // -| #L #K #V #W #U #i #_ #_ #_ #_ #k0 #H destruct -| #L #K #W #V #U #i #_ #_ #_ #_ #k0 #H destruct -| #I #L #V #W #T #U #_ #_ #_ #_ #k0 #H destruct -| #L #V #W #T #U #_ #_ #_ #_ #k0 #H destruct -| #L #V #W #T #U #_ #_ #_ #_ #k0 #H destruct -| #L #T #U #_ #_ #k0 #H destruct -| #L #T #U1 #U2 #V2 #_ #HU12 #_ #IHTU1 #_ #k0 #H destruct - lapply (IHTU1 ??) -IHTU1 [ // | skip ] #Hk0 - lapply (cpcs_trans … Hk0 … HU12) -U1 // -] -qed. - -(* Basic_1: was: ty3_gen_sort *) -lemma nta_inv_sort1: ∀h,L,U,k. ⦃h, L⦄ ⊢ ⋆k : U → L ⊢ ⋆(next h k) ⬌* U. -/2 width=3/ qed-. - -fact nta_inv_lref1_aux: ∀h,L,T,U. ⦃h, L⦄ ⊢ T : U → ∀j. T = #j → - (∃∃K,V,W,U0. ⇩[0, j] L ≡ K. ⓓV & ⦃h, K⦄ ⊢ V : W & - ⇧[0, j + 1] W ≡ U0 & L ⊢ U0 ⬌* U - ) ∨ - (∃∃K,W,V,U0. ⇩[0, j] L ≡ K. ⓛW & ⦃h, K⦄ ⊢ W : V & - ⇧[0, j + 1] W ≡ U0 & L ⊢ U0 ⬌* U - ). -#h #L #T #U #H elim H -L -T -U -[ #L #k #j #H destruct -| #L #K #V #W #U #i #HLK #HVW #HWU #_ #j #H destruct /3 width=8/ -| #L #K #W #V #U #i #HLK #HWV #HWU #_ #j #H destruct /3 width=8/ -| #I #L #V #W #T #U #_ #_ #_ #_ #j #H destruct -| #L #V #W #T #U #_ #_ #_ #_ #j #H destruct -| #L #V #W #T #U #_ #_ #_ #_ #j #H destruct -| #L #T #U #_ #_ #j #H destruct -| #L #T #U1 #U2 #V2 #_ #HU12 #_ #IHTU1 #_ #j #H destruct - elim (IHTU1 ??) -IHTU1 [4: // |2: skip ] * #K #V #W #U0 #HLK #HVW #HWU0 #HU01 - lapply (cpcs_trans … HU01 … HU12) -U1 /3 width=8/ -] -qed. - -(* Basic_1: was ty3_gen_lref *) -lemma nta_inv_lref1: ∀h,L,U,i. ⦃h, L⦄ ⊢ #i : U → - (∃∃K,V,W,U0. ⇩[0, i] L ≡ K. ⓓV & ⦃h, K⦄ ⊢ V : W & - ⇧[0, i + 1] W ≡ U0 & L ⊢ U0 ⬌* U - ) ∨ - (∃∃K,W,V,U0. ⇩[0, i] L ≡ K. ⓛW & ⦃h, K⦄ ⊢ W : V & - ⇧[0, i + 1] W ≡ U0 & L ⊢ U0 ⬌* U - ). -/2 width=3/ qed-. - -(* Basic_1: was: ty3_gen_bind *) -lemma nta_inv_bind1: ∀h,I,L,Y,X,U. ⦃h, L⦄ ⊢ ⓑ{I}Y.X : U → - ∃∃Z1,Z2. ⦃h, L⦄ ⊢ Y : Z1 & ⦃h, L.ⓑ{I}Y⦄ ⊢ X : Z2 & - L ⊢ ⓑ{I}Y.Z2 ⬌* U. -#h #I #L #Y #X #U #H -elim (ntaa_inv_bind1 … (nta_ntaa … H)) -H /3 width=3 by ntaa_nta, ex3_2_intro/ -qed-. - -fact nta_inv_cast1_aux: ∀h,L,T,U. ⦃h, L⦄ ⊢ T : U → ∀X,Y. T = ⓝY.X → - ⦃h, L⦄ ⊢ X : Y ∧ L ⊢ Y ⬌* U. -#h #L #T #U #H elim H -L -T -U -[ #L #k #X #Y #H destruct -| #L #K #V #W #U #i #_ #_ #_ #_ #X #Y #H destruct -| #L #K #W #V #U #i #_ #_ #_ #_ #X #Y #H destruct -| #I #L #V #W #T #U #_ #_ #_ #_ #X #Y #H destruct -| #L #V #W #T #U #_ #_ #_ #_ #X #Y #H destruct -| #L #V #W #T #U #_ #_ #_ #_ #X #Y #H destruct -| #L #T #U #HTU #_ #X #Y #H destruct /2 width=1/ -| #L #T #U1 #U2 #V2 #_ #HU12 #_ #IHTU1 #_ #X #Y #H destruct - elim (IHTU1 ???) -IHTU1 [4: // |2,3: skip ] #HXY #HU1 - lapply (cpcs_trans … HU1 … HU12) -U1 /2 width=1/ -] -qed. - -(* Basic_1: was: ty3_gen_cast *) -lemma nta_inv_cast1: ∀h,L,X,Y,U. ⦃h, L⦄ ⊢ ⓝY.X : U → ⦃h, L⦄ ⊢ X : Y ∧ L ⊢ Y ⬌* U. -/2 width=3/ qed-. - -(* Advanced forvard lemmas **************************************************) - -fact nta_fwd_pure1_aux: ∀h,L,T,U. ⦃h, L⦄ ⊢ T : U → ∀X,Y. T = ⓐY.X → - ∃∃V,W. ⦃h, L⦄ ⊢ Y : W & ⦃h, L⦄ ⊢ X : V & L ⊢ ⓐY.V ⬌* U. -#h #L #T #U #H elim H -L -T -U -[ #L #k #X #Y #H destruct -| #L #K #V #W #U #i #_ #_ #_ #_ #X #Y #H destruct -| #L #K #W #V #U #i #_ #_ #_ #_ #X #Y #H destruct -| #I #L #V #W #T #U #_ #_ #_ #_ #X #Y #H destruct -| #L #V #W #T #U #HVW #HTU #_ #_ #X #Y #H destruct /2 width=3/ -| #L #V #W #T #U #HTU #_ #_ #IHUW #X #Y #H destruct - elim (IHUW U Y ?) -IHUW // /2 width=3/ -| #L #T #U #_ #_ #X #Y #H destruct -| #L #T #U1 #U2 #V2 #_ #HU12 #_ #IHTU1 #_ #X #Y #H destruct - elim (IHTU1 ???) -IHTU1 [4: // |2,3: skip ] #V #W #HYW #HXV #HU1 - lapply (cpcs_trans … HU1 … HU12) -U1 /2 width=3/ -] -qed. - -lemma nta_fwd_pure1: ∀h,L,X,Y,U. ⦃h, L⦄ ⊢ ⓐY.X : U → - ∃∃V,W. ⦃h, L⦄ ⊢ Y : W & ⦃h, L⦄ ⊢ X : V & L ⊢ ⓐY.V ⬌* U. -/2 width=3/ qed-. - -(* Basic_1: was: ty3_correct *) -lemma nta_fwd_correct: ∀h,L,T,U. ⦃h, L⦄ ⊢ T : U → ∃T0. ⦃h, L⦄ ⊢ U : T0. -#h #L #T #U #H -elim (ntaa_fwd_correct … (nta_ntaa … H)) -H /3 width=2 by ntaa_nta, ex_intro/ -qed-. - -(* Advanced properties ******************************************************) - -(* Basic_1: was: ty3_appl *) -lemma nta_appl_old: ∀h,L,V,W,T,U. ⦃h, L⦄ ⊢ V : W → ⦃h, L⦄ ⊢ T : ⓛW.U → - ⦃h, L⦄ ⊢ ⓐV.T : ⓐV.ⓛW.U. -#h #L #V #W #T #U #HVW #HTU -elim (nta_fwd_correct … HTU) #X #H -elim (nta_inv_bind1 … H) -H /4 width=2/ -qed. - -(* Properties on relocation *************************************************) - -(* Basic_1: was: ty3_lift *) -lemma nta_lift: ∀h,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 : U1 → ∀L2,d,e. ⇩[d, e] L2 ≡ L1 → - ∀T2. ⇧[d, e] T1 ≡ T2 → ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃h, L2⦄ ⊢ T2 : U2. -/4 width=9 by ntaa_nta, nta_ntaa, ntaa_lift/ qed.