X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flpx_sn.ma;h=977fd887b5e41fe6d1a582b5e4f14fef5c82404b;hb=dffdece065d12d9961a6c3f1222f6d112030336f;hp=eb640da891b1a9f7b97b3a91db504b5d8da0820c;hpb=87fbbf33fcc2ed91cc8b8a08e1c378ef49ac723d;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn.ma index eb640da89..977fd887b 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn.ma @@ -16,16 +16,16 @@ include "basic_2/grammar/lenv_length.ma". (* SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS *********) -inductive lpx_sn (R:relation4 bind2 lenv term term): relation lenv ≝ +inductive lpx_sn (R:relation3 lenv term term): relation lenv ≝ | lpx_sn_atom: lpx_sn R (⋆) (⋆) | lpx_sn_pair: ∀I,K1,K2,V1,V2. - lpx_sn R K1 K2 → R I K1 V1 V2 → - lpx_sn R (K1.ⓑ{I}V1) (K2.ⓑ{I}V2) + lpx_sn R K1 K2 → R K1 V1 V2 → + lpx_sn R (K1. ⓑ{I} V1) (K2. ⓑ{I} V2) . (* Basic properties *********************************************************) -lemma lpx_sn_refl: ∀R. (∀I,L. reflexive ? (R I L)) → reflexive … (lpx_sn R). +lemma lpx_sn_refl: ∀R. (∀L. reflexive ? (R L)) → reflexive … (lpx_sn R). #R #HR #L elim L -L /2 width=1 by lpx_sn_atom, lpx_sn_pair/ qed-. @@ -41,16 +41,16 @@ qed-. lemma lpx_sn_inv_atom1: ∀R,L2. lpx_sn R (⋆) L2 → L2 = ⋆. /2 width=4 by lpx_sn_inv_atom1_aux/ qed-. -fact lpx_sn_inv_pair1_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K1,V1. L1 = K1.ⓑ{I}V1 → - ∃∃K2,V2. lpx_sn R K1 K2 & R I K1 V1 V2 & L2 = K2.ⓑ{I}V2. +fact lpx_sn_inv_pair1_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K1,V1. L1 = K1. ⓑ{I} V1 → + ∃∃K2,V2. lpx_sn R K1 K2 & R K1 V1 V2 & L2 = K2. ⓑ{I} V2. #R #L1 #L2 * -L1 -L2 [ #J #K1 #V1 #H destruct | #I #K1 #K2 #V1 #V2 #HK12 #HV12 #J #L #W #H destruct /2 width=5 by ex3_2_intro/ ] qed-. -lemma lpx_sn_inv_pair1: ∀R,I,K1,V1,L2. lpx_sn R (K1.ⓑ{I}V1) L2 → - ∃∃K2,V2. lpx_sn R K1 K2 & R I K1 V1 V2 & L2 = K2.ⓑ{I}V2. +lemma lpx_sn_inv_pair1: ∀R,I,K1,V1,L2. lpx_sn R (K1. ⓑ{I} V1) L2 → + ∃∃K2,V2. lpx_sn R K1 K2 & R K1 V1 V2 & L2 = K2. ⓑ{I} V2. /2 width=3 by lpx_sn_inv_pair1_aux/ qed-. fact lpx_sn_inv_atom2_aux: ∀R,L1,L2. lpx_sn R L1 L2 → L2 = ⋆ → L1 = ⋆. @@ -63,21 +63,21 @@ qed-. lemma lpx_sn_inv_atom2: ∀R,L1. lpx_sn R L1 (⋆) → L1 = ⋆. /2 width=4 by lpx_sn_inv_atom2_aux/ qed-. -fact lpx_sn_inv_pair2_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K2,V2. L2 = K2.ⓑ{I}V2 → - ∃∃K1,V1. lpx_sn R K1 K2 & R I K1 V1 V2 & L1 = K1.ⓑ{I}V1. +fact lpx_sn_inv_pair2_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K2,V2. L2 = K2. ⓑ{I} V2 → + ∃∃K1,V1. lpx_sn R K1 K2 & R K1 V1 V2 & L1 = K1. ⓑ{I} V1. #R #L1 #L2 * -L1 -L2 [ #J #K2 #V2 #H destruct | #I #K1 #K2 #V1 #V2 #HK12 #HV12 #J #K #W #H destruct /2 width=5 by ex3_2_intro/ ] qed-. -lemma lpx_sn_inv_pair2: ∀R,I,L1,K2,V2. lpx_sn R L1 (K2.ⓑ{I}V2) → - ∃∃K1,V1. lpx_sn R K1 K2 & R I K1 V1 V2 & L1 = K1.ⓑ{I}V1. +lemma lpx_sn_inv_pair2: ∀R,I,L1,K2,V2. lpx_sn R L1 (K2. ⓑ{I} V2) → + ∃∃K1,V1. lpx_sn R K1 K2 & R K1 V1 V2 & L1 = K1. ⓑ{I} V1. /2 width=3 by lpx_sn_inv_pair2_aux/ qed-. lemma lpx_sn_inv_pair: ∀R,I1,I2,L1,L2,V1,V2. lpx_sn R (L1.ⓑ{I1}V1) (L2.ⓑ{I2}V2) → - ∧∧ lpx_sn R L1 L2 & R I1 L1 V1 V2 & I1 = I2. + ∧∧ lpx_sn R L1 L2 & R L1 V1 V2 & I1 = I2. #R #I1 #I2 #L1 #L2 #V1 #V2 #H elim (lpx_sn_inv_pair1 … H) -H #L0 #V0 #HL10 #HV10 #H destruct /2 width=1 by and3_intro/ qed-.