X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fetc%2Fcsup%2Fcsup.etc;fp=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fetc%2Fcsup%2Fcsup.etc;h=0000000000000000000000000000000000000000;hb=e8998d29ab83e7b6aa495a079193705b2f6743d3;hp=dcfe086e967e438632075d84f27e83f573b49ddb;hpb=bde429ac54e48de74b3d8b1df72dfcb86aa9bae5;p=helm.git diff --git a/matita/matita/contribs/lambda_delta/basic_2/etc/csup/csup.etc b/matita/matita/contribs/lambda_delta/basic_2/etc/csup/csup.etc deleted file mode 100644 index dcfe086e9..000000000 --- a/matita/matita/contribs/lambda_delta/basic_2/etc/csup/csup.etc +++ /dev/null @@ -1,157 +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 *) -(* *) -(**************************************************************************) - -notation "hvbox( ⦃ L1, break T1 ⦄ > break ⦃ L2 , break T2 ⦄ )" - non associative with precedence 45 - for @{ 'SupTerm $L1 $T1 $L2 $T2 }. - -include "basic_2/substitution/ldrop.ma". - -(* SUPCLOSURE ***************************************************************) - -inductive csup: bi_relation lenv term ≝ -| csup_lref : ∀I,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → csup L (#i) K V -| csup_bind_sn: ∀a,I,L,V,T. csup L (ⓑ{a,I}V.T) L V -| csup_bind_dx: ∀a,I,L,V,T. csup L (ⓑ{a,I}V.T) (L.ⓑ{I}V) T -| csup_flat_sn: ∀I,L,V,T. csup L (ⓕ{I}V.T) L V -| csup_flat_dx: ∀I,L,V,T. csup L (ⓕ{I}V.T) L T -. - -interpretation - "structural predecessor (closure)" - 'SupTerm L1 T1 L2 T2 = (csup L1 T1 L2 T2). - -(* Basic inversion lemmas ***************************************************) - -fact csup_inv_atom1_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → ∀J. T1 = ⓪{J} → - ∃∃I,i. ⇩[0, i] L1 ≡ L2.ⓑ{I}T2 & J = LRef i. -#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2 -[ #I #L #K #V #i #HLK #J #H destruct /2 width=4/ -| #a #I #L #V #T #J #H destruct -| #a #I #L #V #T #J #H destruct -| #I #L #V #T #J #H destruct -| #I #L #V #T #J #H destruct -] -qed-. - -lemma csup_inv_atom1: ∀J,L1,L2,T2. ⦃L1, ⓪{J}⦄ > ⦃L2, T2⦄ → - ∃∃I,i. ⇩[0, i] L1 ≡ L2.ⓑ{I}T2 & J = LRef i. -/2 width=3 by csup_inv_atom1_aux/ qed-. - -fact csup_inv_bind1_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → - ∀b,J,W,U. T1 = ⓑ{b,J}W.U → - (L2 = L1 ∧ T2 = W) ∨ - (L2 = L1.ⓑ{J}W ∧ T2 = U). -#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2 -[ #I #L #K #V #i #_ #b #J #W #U #H destruct -| #a #I #L #V #T #b #J #W #U #H destruct /3 width=1/ -| #a #I #L #V #T #b #J #W #U #H destruct /3 width=1/ -| #I #L #V #T #b #J #W #U #H destruct -| #I #L #V #T #b #J #W #U #H destruct -] -qed-. - -lemma csup_inv_bind1: ∀b,J,L1,L2,W,U,T2. ⦃L1, ⓑ{b,J}W.U⦄ > ⦃L2, T2⦄ → - (L2 = L1 ∧ T2 = W) ∨ - (L2 = L1.ⓑ{J}W ∧ T2 = U). -/2 width=4 by csup_inv_bind1_aux/ qed-. - -fact csup_inv_flat1_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → - ∀J,W,U. T1 = ⓕ{J}W.U → - L2 = L1 ∧ (T2 = W ∨ T2 = U). -#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2 -[ #I #L #K #V #i #_ #J #W #U #H destruct -| #a #I #L #V #T #J #W #U #H destruct -| #a #I #L #V #T #J #W #U #H destruct -| #I #L #V #T #J #W #U #H destruct /3 width=1/ -| #I #L #V #T #J #W #U #H destruct /3 width=1/ -] -qed-. - -lemma csup_inv_flat1: ∀J,L1,L2,W,U,T2. ⦃L1, ⓕ{J}W.U⦄ > ⦃L2, T2⦄ → - L2 = L1 ∧ (T2 = W ∨ T2 = U). -/2 width=4 by csup_inv_flat1_aux/ qed-. - -(* Basic forward lemmas *****************************************************) - -lemma csup_fwd_cw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → #{L2, T2} < #{L1, T1}. -#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2 /width=1/ /2 width=4 by ldrop_pair2_fwd_cw/ -qed-. - -lemma csup_fwd_ldrop: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → - ∃i. ⇩[0, i] L1 ≡ L2 ∨ ⇩[0, i] L2 ≡ L1. -#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2 /3 width=2/ /4 width=2/ -#I #L1 #K1 #V1 #i #HLK1 -lapply (ldrop_fwd_ldrop2 … HLK1) -HLK1 /3 width=2/ -qed-. - -(* Advanced forward lemmas **************************************************) - -lemma lift_csup_trans_eq: ∀T1,U1,d,e. ⇧[d, e] T1 ≡ U1 → - ∀L,U2. ⦃L, U1⦄ > ⦃L, U2⦄ → - ∃T2. ⇧[d, e] T2 ≡ U2. -#T1 #U1 #d #e * -T1 -U1 -d -e -[5: #a #I #V1 #W1 #T1 #U1 #d #e #HVW1 #_ #L #X #H - elim (csup_inv_bind1 … H) -H * - [ #_ #H destruct /2 width=2/ - | #H elim (discr_lpair_x_xy … H) - ] -|6: #I #V1 #W1 #T1 #U1 #d #e #HVW1 #HUT1 #L #X #H - elim (csup_inv_flat1 … H) -H #_ * #H destruct /2 width=2/ -] -#i #d #e [2,3: #_ ] #L #X #H -elim (csup_inv_atom1 … H) -H #I #j #HL #H destruct -lapply (ldrop_pair2_fwd_cw … HL X) -HL #H -elim (lt_refl_false … H) -qed-. -(* -lemma lift_csup_trans_gt: ∀L1,L2,U1,U2. ⦃L1, U1⦄ > ⦃L2, U2⦄ → - ⇩[0, 1] L2 ≡ L1 → ∀T1,d,e. ⇧[d, e] T1 ≡ U1 → - ∃T2. ⇧[d + 1, e] T2 ≡ U2. -#L1 #L2 #U1 #U2 * -L1 -L2 -U1 -U2 -[ #I #L1 #K1 #V #i #HLK1 #HKL1 - lapply (ldrop_fwd_lw … HLK1) -HLK1 #HLK1 - lapply (ldrop_fwd_lw … HKL1) -HKL1 #HKL1 - lapply (transitive_le … HLK1 HKL1) -L1 normalize #H - - -| #a -| #a -] -#I #L1 #W1 #U1 #HL1 - - - - #X #d #e #H - lapply (ldrop_inv_refl … HL1) -HL1 -| #a #I #L1 #W1 #U1 #j #HL1 #X #d #e #H - lapply (ldrop_inv_ldrop1 … HL1) - - elim (lift_inv_bind2 … H) -H #W2 #U2 #HW21 #HU21 #H destruct - - - /3 width=2/ /4 width=2/ - -*) - - - -(* Advanced inversion lemmas ************************************************) - -lemma csup_inv_lref2_be: ∀L,U,i. ⦃L, U⦄ > ⦃L, #i⦄ → - ∀T,d,e. ⇧[d, e] T ≡ U → d ≤ i → i < d + e → ⊥. -#L #U #i #H #T #d #e #HTU #Hdi #Hide -elim (lift_csup_trans_eq … HTU … H) -H -T #T #H -elim (lift_inv_lref2_be … H ? ?) // -qed-.