X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Fllpx_sn_ldrop.ma;h=313ddd4e06180d64b8ed4b072c09825de580b50c;hb=f282b35b958c9602fb1f47e5677b5805a046ac76;hp=49ee69f7cf4b04113fe725e57ae712829c3ee0dc;hpb=cb5ca7ea4e826e9331eabeaea44353caab00071e;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/llpx_sn_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/llpx_sn_ldrop.ma index 49ee69f7c..313ddd4e0 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/llpx_sn_ldrop.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/llpx_sn_ldrop.ma @@ -23,7 +23,7 @@ lemma llpx_sn_fwd_lref_dx: ∀R,L1,L2,d,i. llpx_sn R d (#i) L1 L2 → ∀I,K2,V2. ⇩[i] L2 ≡ K2.ⓑ{I}V2 → i < d ∨ ∃∃K1,V1. ⇩[i] L1 ≡ K1.ⓑ{I}V1 & llpx_sn R 0 V1 K1 K2 & - R K1 V1 V2 & d ≤ i. + R I K1 V1 V2 & d ≤ i. #R #L1 #L2 #d #i #H #I #K2 #V2 #HLK2 elim (llpx_sn_fwd_lref … H) -H [ * || * ] [ #_ #H elim (lt_refl_false i) lapply (ldrop_fwd_length_lt2 … HLK2) -HLK2 @@ -39,7 +39,7 @@ lemma llpx_sn_fwd_lref_sn: ∀R,L1,L2,d,i. llpx_sn R d (#i) L1 L2 → ∀I,K1,V1. ⇩[i] L1 ≡ K1.ⓑ{I}V1 → i < d ∨ ∃∃K2,V2. ⇩[i] L2 ≡ K2.ⓑ{I}V2 & llpx_sn R 0 V1 K1 K2 & - R K1 V1 V2 & d ≤ i. + R I K1 V1 V2 & d ≤ i. #R #L1 #L2 #d #i #H #I #K1 #V1 #HLK1 elim (llpx_sn_fwd_lref … H) -H [ * || * ] [ #H #_ elim (lt_refl_false i) lapply (ldrop_fwd_length_lt2 … HLK1) -HLK1 @@ -56,7 +56,7 @@ qed-. lemma llpx_sn_inv_lref_ge_dx: ∀R,L1,L2,d,i. llpx_sn R d (#i) L1 L2 → d ≤ i → ∀I,K2,V2. ⇩[i] L2 ≡ K2.ⓑ{I}V2 → ∃∃K1,V1. ⇩[i] L1 ≡ K1.ⓑ{I}V1 & - llpx_sn R 0 V1 K1 K2 & R K1 V1 V2. + llpx_sn R 0 V1 K1 K2 & R I K1 V1 V2. #R #L1 #L2 #d #i #H #Hdi #I #K2 #V2 #HLK2 elim (llpx_sn_fwd_lref_dx … H … HLK2) -L2 [ #H elim (ylt_yle_false … H Hdi) | * /2 width=5 by ex3_2_intro/ @@ -66,7 +66,7 @@ qed-. lemma llpx_sn_inv_lref_ge_sn: ∀R,L1,L2,d,i. llpx_sn R d (#i) L1 L2 → d ≤ i → ∀I,K1,V1. ⇩[i] L1 ≡ K1.ⓑ{I}V1 → ∃∃K2,V2. ⇩[i] L2 ≡ K2.ⓑ{I}V2 & - llpx_sn R 0 V1 K1 K2 & R K1 V1 V2. + llpx_sn R 0 V1 K1 K2 & R I K1 V1 V2. #R #L1 #L2 #d #i #H #Hdi #I #K1 #V1 #HLK1 elim (llpx_sn_fwd_lref_sn … H … HLK1) -L1 [ #H elim (ylt_yle_false … H Hdi) | * /2 width=5 by ex3_2_intro/ @@ -76,7 +76,7 @@ qed-. lemma llpx_sn_inv_lref_ge_bi: ∀R,L1,L2,d,i. llpx_sn R d (#i) L1 L2 → d ≤ i → ∀I1,I2,K1,K2,V1,V2. ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 → - ∧∧ I1 = I2 & llpx_sn R 0 V1 K1 K2 & R K1 V1 V2. + ∧∧ I1 = I2 & llpx_sn R 0 V1 K1 K2 & R I1 K1 V1 V2. #R #L1 #L2 #d #i #HL12 #Hdi #I1 #I2 #K1 #K2 #V1 #V2 #HLK1 #HLK2 elim (llpx_sn_inv_lref_ge_sn … HL12 … HLK1) // -L1 -d #J #Y #HY lapply (ldrop_mono … HY … HLK2) -L2 -i #H destruct /2 width=1 by and3_intro/ @@ -84,7 +84,7 @@ qed-. fact llpx_sn_inv_S_aux: ∀R,L1,L2,T,d0. llpx_sn R d0 T L1 L2 → ∀d. d0 = d + 1 → ∀K1,K2,I,V1,V2. ⇩[d] L1 ≡ K1.ⓑ{I}V1 → ⇩[d] L2 ≡ K2.ⓑ{I}V2 → - llpx_sn R 0 V1 K1 K2 → R K1 V1 V2 → llpx_sn R d T L1 L2. + llpx_sn R 0 V1 K1 K2 → R I K1 V1 V2 → llpx_sn R d T L1 L2. #R #L1 #L2 #T #d0 #H elim H -L1 -L2 -T -d0 /2 width=1 by llpx_sn_gref, llpx_sn_free, llpx_sn_sort/ [ #L1 #L2 #d0 #i #HL12 #Hid #d #H #K1 #K2 #I #V1 #V2 #HLK1 #HLK2 #HK12 #HV12 destruct @@ -101,10 +101,10 @@ qed-. lemma llpx_sn_inv_S: ∀R,L1,L2,T,d. llpx_sn R (d + 1) T L1 L2 → ∀K1,K2,I,V1,V2. ⇩[d] L1 ≡ K1.ⓑ{I}V1 → ⇩[d] L2 ≡ K2.ⓑ{I}V2 → - llpx_sn R 0 V1 K1 K2 → R K1 V1 V2 → llpx_sn R d T L1 L2. + llpx_sn R 0 V1 K1 K2 → R I K1 V1 V2 → llpx_sn R d T L1 L2. /2 width=9 by llpx_sn_inv_S_aux/ qed-. -lemma llpx_sn_inv_bind_O: ∀R. (∀L. reflexive … (R L)) → +lemma llpx_sn_inv_bind_O: ∀R. (∀I,L. reflexive … (R I L)) → ∀a,I,L1,L2,V,T. llpx_sn R 0 (ⓑ{a,I}V.T) L1 L2 → llpx_sn R 0 V L1 L2 ∧ llpx_sn R 0 T (L1.ⓑ{I}V) (L2.ⓑ{I}V). #R #HR #a #I #L1 #L2 #V #T #H elim (llpx_sn_inv_bind … H) -H @@ -113,7 +113,7 @@ qed-. (* More advanced forward lemmas *********************************************) -lemma llpx_sn_fwd_bind_O_dx: ∀R. (∀L. reflexive … (R L)) → +lemma llpx_sn_fwd_bind_O_dx: ∀R. (∀I,L. reflexive … (R I L)) → ∀a,I,L1,L2,V,T. llpx_sn R 0 (ⓑ{a,I}V.T) L1 L2 → llpx_sn R 0 T (L1.ⓑ{I}V) (L2.ⓑ{I}V). #R #HR #a #I #L1 #L2 #V #T #H elim (llpx_sn_inv_bind_O … H) -H // @@ -122,10 +122,10 @@ qed-. (* Advanced properties ******************************************************) lemma llpx_sn_bind_repl_O: ∀R,I,L1,L2,V1,V2,T. llpx_sn R 0 T (L1.ⓑ{I}V1) (L2.ⓑ{I}V2) → - ∀J,W1,W2. llpx_sn R 0 W1 L1 L2 → R L1 W1 W2 → llpx_sn R 0 T (L1.ⓑ{J}W1) (L2.ⓑ{J}W2). + ∀J,W1,W2. llpx_sn R 0 W1 L1 L2 → R J L1 W1 W2 → llpx_sn R 0 T (L1.ⓑ{J}W1) (L2.ⓑ{J}W2). /3 width=9 by llpx_sn_bind_repl_SO, llpx_sn_inv_S/ qed-. -lemma llpx_sn_dec: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) → +lemma llpx_sn_dec: ∀R. (∀I,L,T1,T2. Decidable (R I L T1 T2)) → ∀T,L1,L2,d. Decidable (llpx_sn R d T L1 L2). #R #HR #T #L1 @(f2_ind … rfw … L1 T) -L1 -T #n #IH #L1 * * @@ -137,7 +137,7 @@ lemma llpx_sn_dec: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) → elim (ldrop_O1_lt … HiL2) #I2 #K2 #V2 #HLK2 elim (ldrop_O1_lt … HiL1) #I1 #K1 #V1 #HLK1 elim (eq_bind2_dec I2 I1) - [ #H2 elim (HR K1 V1 V2) -HR + [ #H2 elim (HR I1 K1 V1 V2) -HR [ #H3 elim (IH K1 V1 … K2 0) destruct /3 width=9 by llpx_sn_lref, ldrop_fwd_rfw, or_introl/ ] @@ -169,7 +169,7 @@ qed-. (* Properties on relocation *************************************************) -lemma llpx_sn_lift_le: ∀R. l_liftable R → +lemma llpx_sn_lift_le: ∀R. (∀I. l_liftable (R I)) → ∀K1,K2,T,d0. llpx_sn R d0 T K1 K2 → ∀L1,L2,d,e. ⇩[Ⓕ, d, e] L1 ≡ K1 → ⇩[Ⓕ, d, e] L2 ≡ K2 → ∀U. ⇧[d, e] T ≡ U → d0 ≤ d → llpx_sn R d0 U L1 L2. @@ -252,7 +252,7 @@ qed-. (* Inversion lemmas on relocation *******************************************) -lemma llpx_sn_inv_lift_le: ∀R. l_deliftable_sn R → +lemma llpx_sn_inv_lift_le: ∀R. (∀I. l_deliftable_sn (R I)) → ∀L1,L2,U,d0. llpx_sn R d0 U L1 L2 → ∀K1,K2,d,e. ⇩[Ⓕ, d, e] L1 ≡ K1 → ⇩[Ⓕ, d, e] L2 ≡ K2 → ∀T. ⇧[d, e] T ≡ U → d0 ≤ d → llpx_sn R d0 T K1 K2. @@ -409,21 +409,21 @@ qed-. (* Inversion lemmas on negated lazy pointwise extension *********************) -lemma nllpx_sn_inv_bind: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) → +lemma nllpx_sn_inv_bind: ∀R. (∀I,L,T1,T2. Decidable (R I L T1 T2)) → ∀a,I,L1,L2,V,T,d. (llpx_sn R d (ⓑ{a,I}V.T) L1 L2 → ⊥) → (llpx_sn R d V L1 L2 → ⊥) ∨ (llpx_sn R (⫯d) T (L1.ⓑ{I}V) (L2.ⓑ{I}V) → ⊥). #R #HR #a #I #L1 #L2 #V #T #d #H elim (llpx_sn_dec … HR V L1 L2 d) /4 width=1 by llpx_sn_bind, or_intror, or_introl/ qed-. -lemma nllpx_sn_inv_flat: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) → +lemma nllpx_sn_inv_flat: ∀R. (∀I,L,T1,T2. Decidable (R I L T1 T2)) → ∀I,L1,L2,V,T,d. (llpx_sn R d (ⓕ{I}V.T) L1 L2 → ⊥) → (llpx_sn R d V L1 L2 → ⊥) ∨ (llpx_sn R d T L1 L2 → ⊥). #R #HR #I #L1 #L2 #V #T #d #H elim (llpx_sn_dec … HR V L1 L2 d) /4 width=1 by llpx_sn_flat, or_intror, or_introl/ qed-. -lemma nllpx_sn_inv_bind_O: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) → +lemma nllpx_sn_inv_bind_O: ∀R. (∀I,L,T1,T2. Decidable (R I L T1 T2)) → ∀a,I,L1,L2,V,T. (llpx_sn R 0 (ⓑ{a,I}V.T) L1 L2 → ⊥) → (llpx_sn R 0 V L1 L2 → ⊥) ∨ (llpx_sn R 0 T (L1.ⓑ{I}V) (L2.ⓑ{I}V) → ⊥). #R #HR #a #I #L1 #L2 #V #T #H elim (llpx_sn_dec … HR V L1 L2 0)