X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Fsubstitution%2Fldrop.ma;h=c7fc055e7cacf84d8c68f64bd3686c951865b562;hb=48b202cd4ccd3ffc10f9a134314f747fdee30d36;hp=d3788f4104ada2e50aaab0737ebc235e0f5c447d;hpb=e4328c9691fa85434acfb24eaedcb15ea2263b28;p=helm.git diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ldrop.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ldrop.ma index d3788f410..c7fc055e7 100644 --- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ldrop.ma +++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ldrop.ma @@ -21,11 +21,11 @@ include "Basic_2/substitution/lift.ma". (* Basic_1: includes: ldrop_skip_bind *) inductive ldrop: nat → nat → relation lenv ≝ | ldrop_atom : ∀d,e. ldrop d e (⋆) (⋆) -| ldrop_pair : ∀L,I,V. ldrop 0 0 (L. 𝕓{I} V) (L. 𝕓{I} V) -| ldrop_ldrop: ∀L1,L2,I,V,e. ldrop 0 e L1 L2 → ldrop 0 (e + 1) (L1. 𝕓{I} V) L2 +| ldrop_pair : ∀L,I,V. ldrop 0 0 (L. ⓑ{I} V) (L. ⓑ{I} V) +| ldrop_ldrop: ∀L1,L2,I,V,e. ldrop 0 e L1 L2 → ldrop 0 (e + 1) (L1. ⓑ{I} V) L2 | ldrop_skip : ∀L1,L2,I,V1,V2,d,e. ldrop d e L1 L2 → ⇧[d,e] V2 ≡ V1 → - ldrop (d + 1) e (L1. 𝕓{I} V1) (L2. 𝕓{I} V2) + ldrop (d + 1) e (L1. ⓑ{I} V1) (L2. ⓑ{I} V2) . interpretation "local slicing" 'RDrop d e L1 L2 = (ldrop d e L1 L2). @@ -60,8 +60,8 @@ lemma ldrop_inv_atom1: ∀d,e,L2. ⇩[d, e] ⋆ ≡ L2 → L2 = ⋆. /2 width=5/ qed-. fact ldrop_inv_O1_aux: ∀d,e,L1,L2. ⇩[d, e] L1 ≡ L2 → d = 0 → - ∀K,I,V. L1 = K. 𝕓{I} V → - (e = 0 ∧ L2 = K. 𝕓{I} V) ∨ + ∀K,I,V. L1 = K. ⓑ{I} V → + (e = 0 ∧ L2 = K. ⓑ{I} V) ∨ (0 < e ∧ ⇩[d, e - 1] K ≡ L2). #d #e #L1 #L2 * -d -e -L1 -L2 [ #d #e #_ #K #I #V #H destruct @@ -71,24 +71,24 @@ fact ldrop_inv_O1_aux: ∀d,e,L1,L2. ⇩[d, e] L1 ≡ L2 → d = 0 → ] qed. -lemma ldrop_inv_O1: ∀e,K,I,V,L2. ⇩[0, e] K. 𝕓{I} V ≡ L2 → - (e = 0 ∧ L2 = K. 𝕓{I} V) ∨ +lemma ldrop_inv_O1: ∀e,K,I,V,L2. ⇩[0, e] K. ⓑ{I} V ≡ L2 → + (e = 0 ∧ L2 = K. ⓑ{I} V) ∨ (0 < e ∧ ⇩[0, e - 1] K ≡ L2). /2 width=3/ qed-. (* Basic_1: was: ldrop_gen_ldrop *) lemma ldrop_inv_ldrop1: ∀e,K,I,V,L2. - ⇩[0, e] K. 𝕓{I} V ≡ L2 → 0 < e → ⇩[0, e - 1] K ≡ L2. + ⇩[0, e] K. ⓑ{I} V ≡ L2 → 0 < e → ⇩[0, e - 1] K ≡ L2. #e #K #I #V #L2 #H #He elim (ldrop_inv_O1 … H) -H * // #H destruct elim (lt_refl_false … He) qed-. fact ldrop_inv_skip1_aux: ∀d,e,L1,L2. ⇩[d, e] L1 ≡ L2 → 0 < d → - ∀I,K1,V1. L1 = K1. 𝕓{I} V1 → + ∀I,K1,V1. L1 = K1. ⓑ{I} V1 → ∃∃K2,V2. ⇩[d - 1, e] K1 ≡ K2 & ⇧[d - 1, e] V2 ≡ V1 & - L2 = K2. 𝕓{I} V2. + L2 = K2. ⓑ{I} V2. #d #e #L1 #L2 * -d -e -L1 -L2 [ #d #e #_ #I #K #V #H destruct | #L #I #V #H elim (lt_refl_false … H) @@ -98,17 +98,17 @@ fact ldrop_inv_skip1_aux: ∀d,e,L1,L2. ⇩[d, e] L1 ≡ L2 → 0 < d → qed. (* Basic_1: was: ldrop_gen_skip_l *) -lemma ldrop_inv_skip1: ∀d,e,I,K1,V1,L2. ⇩[d, e] K1. 𝕓{I} V1 ≡ L2 → 0 < d → +lemma ldrop_inv_skip1: ∀d,e,I,K1,V1,L2. ⇩[d, e] K1. ⓑ{I} V1 ≡ L2 → 0 < d → ∃∃K2,V2. ⇩[d - 1, e] K1 ≡ K2 & ⇧[d - 1, e] V2 ≡ V1 & - L2 = K2. 𝕓{I} V2. + L2 = K2. ⓑ{I} V2. /2 width=3/ qed-. fact ldrop_inv_skip2_aux: ∀d,e,L1,L2. ⇩[d, e] L1 ≡ L2 → 0 < d → - ∀I,K2,V2. L2 = K2. 𝕓{I} V2 → + ∀I,K2,V2. L2 = K2. ⓑ{I} V2 → ∃∃K1,V1. ⇩[d - 1, e] K1 ≡ K2 & ⇧[d - 1, e] V2 ≡ V1 & - L1 = K1. 𝕓{I} V1. + L1 = K1. ⓑ{I} V1. #d #e #L1 #L2 * -d -e -L1 -L2 [ #d #e #_ #I #K #V #H destruct | #L #I #V #H elim (lt_refl_false … H) @@ -118,9 +118,9 @@ fact ldrop_inv_skip2_aux: ∀d,e,L1,L2. ⇩[d, e] L1 ≡ L2 → 0 < d → qed. (* Basic_1: was: ldrop_gen_skip_r *) -lemma ldrop_inv_skip2: ∀d,e,I,L1,K2,V2. ⇩[d, e] L1 ≡ K2. 𝕓{I} V2 → 0 < d → +lemma ldrop_inv_skip2: ∀d,e,I,L1,K2,V2. ⇩[d, e] L1 ≡ K2. ⓑ{I} V2 → 0 < d → ∃∃K1,V1. ⇩[d - 1, e] K1 ≡ K2 & ⇧[d - 1, e] V2 ≡ V1 & - L1 = K1. 𝕓{I} V1. + L1 = K1. ⓑ{I} V1. /2 width=3/ qed-. (* Basic properties *********************************************************) @@ -131,15 +131,15 @@ lemma ldrop_refl: ∀L. ⇩[0, 0] L ≡ L. qed. lemma ldrop_ldrop_lt: ∀L1,L2,I,V,e. - ⇩[0, e - 1] L1 ≡ L2 → 0 < e → ⇩[0, e] L1. 𝕓{I} V ≡ L2. + ⇩[0, e - 1] L1 ≡ L2 → 0 < e → ⇩[0, e] L1. ⓑ{I} V ≡ L2. #L1 #L2 #I #V #e #HL12 #He >(plus_minus_m_m e 1) // /2 width=1/ qed. lemma ldrop_lsubs_ldrop1_abbr: ∀L1,L2,d,e. L1 [d, e] ≼ L2 → - ∀K1,V,i. ⇩[0, i] L1 ≡ K1. 𝕓{Abbr} V → + ∀K1,V,i. ⇩[0, i] L1 ≡ K1. ⓓV → d ≤ i → i < d + e → ∃∃K2. K1 [0, d + e - i - 1] ≼ K2 & - ⇩[0, i] L2 ≡ K2. 𝕓{Abbr} V. + ⇩[0, i] L2 ≡ K2. ⓓV. #L1 #L2 #d #e #H elim H -L1 -L2 -d -e [ #d #e #K1 #V #i #H lapply (ldrop_inv_atom1 … H) -H #H destruct @@ -167,7 +167,7 @@ qed. (* Basic forvard lemmas *****************************************************) (* Basic_1: was: ldrop_S *) -lemma ldrop_fwd_ldrop2: ∀L1,I2,K2,V2,e. ⇩[O, e] L1 ≡ K2. 𝕓{I2} V2 → +lemma ldrop_fwd_ldrop2: ∀L1,I2,K2,V2,e. ⇩[O, e] L1 ≡ K2. ⓑ{I2} V2 → ⇩[O, e + 1] L1 ≡ K2. #L1 elim L1 -L1 [ #I2 #K2 #V2 #e #H lapply (ldrop_inv_atom1 … H) -H #H destruct @@ -188,7 +188,7 @@ lemma ldrop_fwd_lw: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → #[L2] ≤ #[L1]. qed-. lemma ldrop_fwd_ldrop2_length: ∀L1,I2,K2,V2,e. - ⇩[0, e] L1 ≡ K2. 𝕓{I2} V2 → e < |L1|. + ⇩[0, e] L1 ≡ K2. ⓑ{I2} V2 → e < |L1|. #L1 elim L1 -L1 [ #I2 #K2 #V2 #e #H lapply (ldrop_inv_atom1 … H) -H #H destruct | #K1 #I1 #V1 #IHL1 #I2 #K2 #V2 #e #H