X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fsubstitution%2Fldrop_ldrop.ma;fp=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fsubstitution%2Fldrop_ldrop.ma;h=0000000000000000000000000000000000000000;hb=e8998d29ab83e7b6aa495a079193705b2f6743d3;hp=07d9c53e41d586f76216b82740190443e3848790;hpb=bde429ac54e48de74b3d8b1df72dfcb86aa9bae5;p=helm.git diff --git a/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop_ldrop.ma b/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop_ldrop.ma deleted file mode 100644 index 07d9c53e4..000000000 --- a/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop_ldrop.ma +++ /dev/null @@ -1,176 +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_lift.ma". -include "basic_2/substitution/ldrop.ma". - -(* DROPPING *****************************************************************) - -(* Main properties **********************************************************) - -(* Basic_1: was: drop_mono *) -theorem ldrop_mono: ∀d,e,L,L1. ⇩[d, e] L ≡ L1 → - ∀L2. ⇩[d, e] L ≡ L2 → L1 = L2. -#d #e #L #L1 #H elim H -d -e -L -L1 -[ #d #e #L2 #H - >(ldrop_inv_atom1 … H) -L2 // -| #K #I #V #L2 #HL12 - <(ldrop_inv_refl … HL12) -L2 // -| #L #K #I #V #e #_ #IHLK #L2 #H - lapply (ldrop_inv_ldrop1 … H ?) -H // /2 width=1/ -| #L #K1 #I #T #V1 #d #e #_ #HVT1 #IHLK1 #X #H - elim (ldrop_inv_skip1 … H ?) -H // (lift_inj … HVT1 … HVT2) -HVT1 -HVT2 - >(IHLK1 … HLK2) -IHLK1 -HLK2 // -] -qed-. - -(* Basic_1: was: drop_conf_ge *) -theorem ldrop_conf_ge: ∀d1,e1,L,L1. ⇩[d1, e1] L ≡ L1 → - ∀e2,L2. ⇩[0, e2] L ≡ L2 → d1 + e1 ≤ e2 → - ⇩[0, e2 - e1] L1 ≡ L2. -#d1 #e1 #L #L1 #H elim H -d1 -e1 -L -L1 -[ #d #e #e2 #L2 #H - >(ldrop_inv_atom1 … H) -L2 // -| // -| #L #K #I #V #e #_ #IHLK #e2 #L2 #H #He2 - lapply (ldrop_inv_ldrop1 … H ?) -H /2 width=2/ #HL2 - minus_minus_comm /3 width=1/ -| #L #K #I #V1 #V2 #d #e #_ #_ #IHLK #e2 #L2 #H #Hdee2 - lapply (transitive_le 1 … Hdee2) // #He2 - lapply (ldrop_inv_ldrop1 … H ?) -H // -He2 #HL2 - lapply (transitive_le (1 + e) … Hdee2) // #Hee2 - @ldrop_ldrop_lt >minus_minus_comm /3 width=1/ (**) (* explicit constructor *) -] -qed. - -(* Note: apparently this was missing in basic_1 *) -theorem ldrop_conf_be: ∀L0,L1,d1,e1. ⇩[d1, e1] L0 ≡ L1 → - ∀L2,e2. ⇩[0, e2] L0 ≡ L2 → d1 ≤ e2 → e2 ≤ d1 + e1 → - ∃∃L. ⇩[0, d1 + e1 - e2] L2 ≡ L & ⇩[0, d1] L1 ≡ L. -#L0 #L1 #d1 #e1 #H elim H -L0 -L1 -d1 -e1 -[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2 width=3/ -| normalize #L #I #V #L2 #e2 #HL2 #_ #He2 - lapply (le_n_O_to_eq … He2) -He2 #H destruct - lapply (ldrop_inv_refl … HL2) -HL2 #H destruct /2 width=3/ -| normalize #L0 #K0 #I #V1 #e1 #HLK0 #IHLK0 #L2 #e2 #H #_ #He21 - lapply (ldrop_inv_O1 … H) -H * * #He2 #HL20 - [ -IHLK0 -He21 destruct plus_plus_comm_23 #_ #_ #IHLK0 #L2 #e2 #H #Hd1e2 #He2de1 - elim (le_inv_plus_l … Hd1e2) #_ #He2 - minus_le_minus_minus_comm // /3 width=3/ - ] -] -qed. - -(* Basic_1: was: drop_trans_ge *) -theorem ldrop_trans_ge: ∀d1,e1,L1,L. ⇩[d1, e1] L1 ≡ L → - ∀e2,L2. ⇩[0, e2] L ≡ L2 → d1 ≤ e2 → ⇩[0, e1 + e2] L1 ≡ L2. -#d1 #e1 #L1 #L #H elim H -d1 -e1 -L1 -L -[ #d #e #e2 #L2 #H - >(ldrop_inv_atom1 … H) -H -L2 // -| // -| /3 width=1/ -| #L1 #L2 #I #V1 #V2 #d #e #H_ #_ #IHL12 #e2 #L #H #Hde2 - lapply (lt_to_le_to_lt 0 … Hde2) // #He2 - lapply (lt_to_le_to_lt … (e + e2) He2 ?) // #Hee2 - lapply (ldrop_inv_ldrop1 … H ?) -H // #HL2 - @ldrop_ldrop_lt // >le_plus_minus // @IHL12 /2 width=1/ (**) (* explicit constructor *) -] -qed. - -(* Basic_1: was: drop_trans_le *) -theorem ldrop_trans_le: ∀d1,e1,L1,L. ⇩[d1, e1] L1 ≡ L → - ∀e2,L2. ⇩[0, e2] L ≡ L2 → e2 ≤ d1 → - ∃∃L0. ⇩[0, e2] L1 ≡ L0 & ⇩[d1 - e2, e1] L0 ≡ L2. -#d1 #e1 #L1 #L #H elim H -d1 -e1 -L1 -L -[ #d #e #e2 #L2 #H - >(ldrop_inv_atom1 … H) -L2 /2 width=3/ -| #K #I #V #e2 #L2 #HL2 #H - lapply (le_n_O_to_eq … H) -H #H destruct /2 width=3/ -| #L1 #L2 #I #V #e #_ #IHL12 #e2 #L #HL2 #H - lapply (le_n_O_to_eq … H) -H #H destruct - elim (IHL12 … HL2 ?) -IHL12 -HL2 // #L0 #H #HL0 - lapply (ldrop_inv_refl … H) -H #H destruct /3 width=5/ -| #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #IHL12 #e2 #L #H #He2d - elim (ldrop_inv_O1 … H) -H * - [ -He2d -IHL12 #H1 #H2 destruct /3 width=5/ - | -HL12 -HV12 #He2 #HL2 - elim (IHL12 … HL2 ?) -L2 [ >minus_le_minus_minus_comm // /3 width=3/ | /2 width=1/ ] - ] -] -qed. - -(* Basic_1: was: drop_conf_rev *) -axiom ldrop_div: ∀e1,L1,L. ⇩[0, e1] L1 ≡ L → ∀e2,L2. ⇩[0, e2] L2 ≡ L → - ∃∃L0. ⇩[0, e1] L0 ≡ L2 & ⇩[e1, e2] L0 ≡ L1. - -(* Basic_1: was: drop_conf_lt *) -lemma ldrop_conf_lt: ∀d1,e1,L,L1. ⇩[d1, e1] L ≡ L1 → - ∀e2,K2,I,V2. ⇩[0, e2] L ≡ K2. ⓑ{I} V2 → - e2 < d1 → let d ≝ d1 - e2 - 1 in - ∃∃K1,V1. ⇩[0, e2] L1 ≡ K1. ⓑ{I} V1 & - ⇩[d, e1] K2 ≡ K1 & ⇧[d, e1] V1 ≡ V2. -#d1 #e1 #L #L1 #H1 #e2 #K2 #I #V2 #H2 #He2d1 -elim (ldrop_conf_le … H1 … H2 ?) -L [2: /2 width=2/] #K #HL1K #HK2 -elim (ldrop_inv_skip1 … HK2 ?) -HK2 [2: /2 width=1/] #K1 #V1 #HK21 #HV12 #H destruct /2 width=5/ -qed. - -lemma ldrop_trans_ge_comm: ∀d1,e1,e2,L1,L2,L. - ⇩[d1, e1] L1 ≡ L → ⇩[0, e2] L ≡ L2 → d1 ≤ e2 → - ⇩[0, e2 + e1] L1 ≡ L2. -#e1 #e1 #e2 >commutative_plus /2 width=5/ -qed. - -lemma ldrop_conf_div: ∀I1,L,K,V1,e1. ⇩[0, e1] L ≡ K. ⓑ{I1} V1 → - ∀I2,V2,e2. ⇩[0, e2] L ≡ K. ⓑ{I2} V2 → - ∧∧ e1 = e2 & I1 = I2 & V1 = V2. -#I1 #L #K #V1 #e1 #HLK1 #I2 #V2 #e2 #HLK2 -elim (le_or_ge e1 e2) #He -[ lapply (ldrop_conf_ge … HLK1 … HLK2 ?) -| lapply (ldrop_conf_ge … HLK2 … HLK1 ?) -] -HLK1 -HLK2 // #HK -lapply (ldrop_fwd_O1_length … HK) #H -elim (discr_minus_x_xy … H) -H -[1,3: normalize H in HK; #HK -lapply (ldrop_inv_refl … HK) -HK #H destruct -lapply (inv_eq_minus_O … H) -H /3 width=1/ -qed-.