X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=inline;f=matita%2Fmatita%2Fcontribs%2Flambda-delta%2FBasic-2%2Fsubstitution%2Flift_lift.ma;fp=matita%2Fmatita%2Fcontribs%2Flambda-delta%2FBasic-2%2Fsubstitution%2Flift_lift.ma;h=0000000000000000000000000000000000000000;hb=0dc8115859d7f482793315493adc0b619236e06c;hp=f9c99457db747c0e0c0b1983e4873c2aa52235fe;hpb=55dc00c1c44cc21c7ae179cb9df03e7446002c46;p=helm.git diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/lift_lift.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/lift_lift.ma deleted file mode 100644 index f9c99457d..000000000 --- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/lift_lift.ma +++ /dev/null @@ -1,159 +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/substitution/lift.ma". - -(* RELOCATION ***************************************************************) - -(* Main properies ***********************************************************) - -(* Basic-1: was: lift_inj *) -theorem lift_inj: ∀d,e,T1,U. ↑[d,e] T1 ≡ U → ∀T2. ↑[d,e] T2 ≡ U → T1 = T2. -#d #e #T1 #U #H elim H -H d e T1 U -[ #k #d #e #X #HX - lapply (lift_inv_sort2 … HX) -HX // -| #i #d #e #Hid #X #HX - lapply (lift_inv_lref2_lt … HX ?) -HX // -| #i #d #e #Hdi #X #HX - lapply (lift_inv_lref2_ge … HX ?) -HX /2/ -| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX - elim (lift_inv_bind2 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/ -| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX - elim (lift_inv_flat2 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/ -] -qed. - -(* Basic-1: was: lift_gen_lift *) -theorem lift_div_le: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T → - ∀d2,e2,T2. ↑[d2 + e1, e2] T2 ≡ T → - d1 ≤ d2 → - ∃∃T0. ↑[d1, e1] T0 ≡ T2 & ↑[d2, e2] T0 ≡ T1. -#d1 #e1 #T1 #T #H elim H -H d1 e1 T1 T -[ #k #d1 #e1 #d2 #e2 #T2 #Hk #Hd12 - lapply (lift_inv_sort2 … Hk) -Hk #Hk destruct -T2 /3/ -| #i #d1 #e1 #Hid1 #d2 #e2 #T2 #Hi #Hd12 - lapply (lt_to_le_to_lt … Hid1 Hd12) -Hd12 #Hid2 - lapply (lift_inv_lref2_lt … Hi ?) -Hi /3/ -| #i #d1 #e1 #Hid1 #d2 #e2 #T2 #Hi #Hd12 - elim (lift_inv_lref2 … Hi) -Hi * #Hid2 #H destruct -T2 - [ -Hd12; lapply (lt_plus_to_lt_l … Hid2) -Hid2 #Hid2 /3/ - | -Hid1; lapply (arith1 … Hid2) -Hid2 #Hid2 - @(ex2_1_intro … #(i - e2)) - [ >le_plus_minus_comm [ @lift_lref_ge @(transitive_le … Hd12) -Hd12 /2/ | -Hd12 /2/ ] - | -Hd12 >(plus_minus_m_m i e2) in ⊢ (? ? ? ? %) /3/ - ] - ] -| #I #W1 #W #U1 #U #d1 #e1 #_ #_ #IHW #IHU #d2 #e2 #T2 #H #Hd12 - lapply (lift_inv_bind2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct -T2; - elim (IHW … HW2 ?) // -IHW HW2 #W0 #HW2 #HW1 - >plus_plus_comm_23 in HU2 #HU2 elim (IHU … HU2 ?) /3 width = 5/ -| #I #W1 #W #U1 #U #d1 #e1 #_ #_ #IHW #IHU #d2 #e2 #T2 #H #Hd12 - lapply (lift_inv_flat2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct -T2; - elim (IHW … HW2 ?) // -IHW HW2 #W0 #HW2 #HW1 - elim (IHU … HU2 ?) /3 width = 5/ -] -qed. - -theorem lift_mono: ∀d,e,T,U1. ↑[d,e] T ≡ U1 → ∀U2. ↑[d,e] T ≡ U2 → U1 = U2. -#d #e #T #U1 #H elim H -H d e T U1 -[ #k #d #e #X #HX - lapply (lift_inv_sort1 … HX) -HX // -| #i #d #e #Hid #X #HX - lapply (lift_inv_lref1_lt … HX ?) -HX // -| #i #d #e #Hdi #X #HX - lapply (lift_inv_lref1_ge … HX ?) -HX // -| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX - elim (lift_inv_bind1 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/ -| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX - elim (lift_inv_flat1 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/ -] -qed. - -(* Basic-1: was: lift_free (left to right) *) -theorem lift_trans_be: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T → - ∀d2,e2,T2. ↑[d2, e2] T ≡ T2 → - d1 ≤ d2 → d2 ≤ d1 + e1 → ↑[d1, e1 + e2] T1 ≡ T2. -#d1 #e1 #T1 #T #H elim H -H d1 e1 T1 T -[ #k #d1 #e1 #d2 #e2 #T2 #HT2 #_ #_ - >(lift_inv_sort1 … HT2) -HT2 // -| #i #d1 #e1 #Hid1 #d2 #e2 #T2 #HT2 #Hd12 #_ - lapply (lt_to_le_to_lt … Hid1 Hd12) -Hd12 #Hid2 - lapply (lift_inv_lref1_lt … HT2 Hid2) /2/ -| #i #d1 #e1 #Hid1 #d2 #e2 #T2 #HT2 #_ #Hd21 - lapply (lift_inv_lref1_ge … HT2 ?) -HT2 - [ @(transitive_le … Hd21 ?) -Hd21 /2/ - | -Hd21 /2/ - ] -| #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd12 #Hd21 - elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; - lapply (IHV12 … HV20 ? ?) // -IHV12 HV20 #HV10 - lapply (IHT12 … HT20 ? ?) /2/ -| #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd12 #Hd21 - elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; - lapply (IHV12 … HV20 ? ?) // -IHV12 HV20 #HV10 - lapply (IHT12 … HT20 ? ?) /2/ -] -qed. - -(* Basic-1: was: lift_d (right to left) *) -theorem lift_trans_le: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T → - ∀d2,e2,T2. ↑[d2, e2] T ≡ T2 → d2 ≤ d1 → - ∃∃T0. ↑[d2, e2] T1 ≡ T0 & ↑[d1 + e2, e1] T0 ≡ T2. -#d1 #e1 #T1 #T #H elim H -H d1 e1 T1 T -[ #k #d1 #e1 #d2 #e2 #X #HX #_ - >(lift_inv_sort1 … HX) -HX /2/ -| #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #_ - lapply (lt_to_le_to_lt … (d1+e2) Hid1 ?) // #Hie2 - elim (lift_inv_lref1 … HX) -HX * #Hid2 #HX destruct -X /4/ -| #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #Hd21 - lapply (transitive_le … Hd21 Hid1) -Hd21 #Hid2 - lapply (lift_inv_lref1_ge … HX ?) -HX /2/ #HX destruct -X; - >plus_plus_comm_23 /4/ -| #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd21 - elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; - elim (IHV12 … HV20 ?) -IHV12 HV20 // - elim (IHT12 … HT20 ?) -IHT12 HT20 /3 width=5/ -| #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd21 - elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; - elim (IHV12 … HV20 ?) -IHV12 HV20 // - elim (IHT12 … HT20 ?) -IHT12 HT20 /3 width=5/ -] -qed. - -(* Basic-1: was: lift_d (left to right) *) -theorem lift_trans_ge: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T → - ∀d2,e2,T2. ↑[d2, e2] T ≡ T2 → d1 + e1 ≤ d2 → - ∃∃T0. ↑[d2 - e1, e2] T1 ≡ T0 & ↑[d1, e1] T0 ≡ T2. -#d1 #e1 #T1 #T #H elim H -H d1 e1 T1 T -[ #k #d1 #e1 #d2 #e2 #X #HX #_ - >(lift_inv_sort1 … HX) -HX /2/ -| #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #Hded - lapply (lt_to_le_to_lt … (d1+e1) Hid1 ?) // #Hid1e - lapply (lt_to_le_to_lt … (d2-e1) Hid1 ?) /2/ #Hid2e - lapply (lt_to_le_to_lt … Hid1e Hded) -Hid1e Hded #Hid2 - lapply (lift_inv_lref1_lt … HX ?) -HX // #HX destruct -X /3/ -| #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #_ - elim (lift_inv_lref1 … HX) -HX * #Hied #HX destruct -X; - [2: >plus_plus_comm_23] /4/ -| #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hded - elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; - elim (IHV12 … HV20 ?) -IHV12 HV20 // - elim (IHT12 … HT20 ?) -IHT12 HT20 /2/ #T -