X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fi_static%2Ftc_lfxs.ma;h=e1dd22673900719167ee343232a6bf4a06422fc4;hb=981599dd384b3424c60297ea3a64ab0af9788ea2;hp=b8976cbd9d46eded64124ba74a948acfb61244db;hpb=86badc0111c3626c4a547d09302acc7e6a179dea;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma index b8976cbd9..e1dd22673 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma @@ -25,40 +25,40 @@ interpretation "iterated extension on referred entries (local environment)" (* Basic properties *********************************************************) -lemma tc_lfxs_step_dx: ∀R,L1,L,T. L1 ⦻**[R, T] L → - ∀L2. L ⦻*[R, T] L2 → L1 ⦻**[R, T] L2. +lemma tc_lfxs_step_dx: ∀R,L1,L,T. L1 ⪤**[R, T] L → + ∀L2. L ⪤*[R, T] L2 → L1 ⪤**[R, T] L2. #R #L1 #L2 #T #HL1 #L2 @step @HL1 (**) (* auto fails *) qed-. -lemma tc_lfxs_step_sn: ∀R,L1,L,T. L1 ⦻*[R, T] L → - ∀L2. L ⦻**[R, T] L2 → L1 ⦻**[R, T] L2. +lemma tc_lfxs_step_sn: ∀R,L1,L,T. L1 ⪤*[R, T] L → + ∀L2. L ⪤**[R, T] L2 → L1 ⪤**[R, T] L2. #R #L1 #L2 #T #HL1 #L2 @TC_strap @HL1 (**) (* auto fails *) qed-. -lemma tc_lfxs_atom: ∀R,I. ⋆ ⦻**[R, ⓪{I}] ⋆. +lemma tc_lfxs_atom: ∀R,I. ⋆ ⪤**[R, ⓪{I}] ⋆. /2 width=1 by inj/ qed. lemma tc_lfxs_sort: ∀R,I,L1,L2,V1,V2,s. - L1 ⦻**[R, ⋆s] L2 → L1.ⓑ{I}V1 ⦻**[R, ⋆s] L2.ⓑ{I}V2. + L1 ⪤**[R, ⋆s] L2 → L1.ⓑ{I}V1 ⪤**[R, ⋆s] L2.ⓑ{I}V2. #R #I #L1 #L2 #V1 #V2 #s #H elim H -L2 /3 width=4 by lfxs_sort, tc_lfxs_step_dx, inj/ qed. lemma tc_lfxs_zero: ∀R. (∀L. reflexive … (R L)) → - ∀I,L1,L2,V. L1 ⦻**[R, V] L2 → - L1.ⓑ{I}V ⦻**[R, #0] L2.ⓑ{I}V. + ∀I,L1,L2,V. L1 ⪤**[R, V] L2 → + L1.ⓑ{I}V ⪤**[R, #0] L2.ⓑ{I}V. #R #HR #I #L1 #L2 #V #H elim H -L2 /3 width=5 by lfxs_zero, tc_lfxs_step_dx, inj/ qed. lemma tc_lfxs_lref: ∀R,I,L1,L2,V1,V2,i. - L1 ⦻**[R, #i] L2 → L1.ⓑ{I}V1 ⦻**[R, #⫯i] L2.ⓑ{I}V2. + L1 ⪤**[R, #i] L2 → L1.ⓑ{I}V1 ⪤**[R, #⫯i] L2.ⓑ{I}V2. #R #I #L1 #L2 #V1 #V2 #i #H elim H -L2 /3 width=4 by lfxs_lref, tc_lfxs_step_dx, inj/ qed. lemma tc_lfxs_gref: ∀R,I,L1,L2,V1,V2,l. - L1 ⦻**[R, §l] L2 → L1.ⓑ{I}V1 ⦻**[R, §l] L2.ⓑ{I}V2. + L1 ⪤**[R, §l] L2 → L1.ⓑ{I}V1 ⪤**[R, §l] L2.ⓑ{I}V2. #R #I #L1 #L2 #V1 #V2 #l #H elim H -L2 /3 width=4 by lfxs_gref, tc_lfxs_step_dx, inj/ qed. @@ -71,7 +71,7 @@ lemma tc_lfxs_sym: ∀R. lexs_frees_confluent R cfull → qed-. lemma tc_lfxs_co: ∀R1,R2. (∀L,T1,T2. R1 L T1 T2 → R2 L T1 T2) → - ∀L1,L2,T. L1 ⦻**[R1, T] L2 → L1 ⦻**[R2, T] L2. + ∀L1,L2,T. L1 ⪤**[R1, T] L2 → L1 ⪤**[R2, T] L2. #R1 #R2 #HR #L1 #L2 #T #H elim H -L2 /4 width=5 by lfxs_co, tc_lfxs_step_dx, inj/ qed-. @@ -79,19 +79,19 @@ qed-. (* Basic inversion lemmas ***************************************************) (* Basic_2A1: uses: TC_lpx_sn_inv_atom1 *) -lemma tc_lfxs_inv_atom_sn: ∀R,I,Y2. ⋆ ⦻**[R, ⓪{I}] Y2 → Y2 = ⋆. +lemma tc_lfxs_inv_atom_sn: ∀R,I,Y2. ⋆ ⪤**[R, ⓪{I}] Y2 → Y2 = ⋆. #R #I #Y2 #H elim H -Y2 /3 width=3 by inj, lfxs_inv_atom_sn/ qed-. (* Basic_2A1: uses: TC_lpx_sn_inv_atom2 *) -lemma tc_lfxs_inv_atom_dx: ∀R,I,Y1. Y1 ⦻**[R, ⓪{I}] ⋆ → Y1 = ⋆. +lemma tc_lfxs_inv_atom_dx: ∀R,I,Y1. Y1 ⪤**[R, ⓪{I}] ⋆ → Y1 = ⋆. #R #I #Y1 #H @(TC_ind_dx ??????? H) -Y1 /3 width=3 by inj, lfxs_inv_atom_dx/ qed-. -lemma tc_lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⦻**[R, ⋆s] Y2 → +lemma tc_lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⪤**[R, ⋆s] Y2 → (Y1 = ⋆ ∧ Y2 = ⋆) ∨ - ∃∃I,L1,L2,V1,V2. L1 ⦻**[R, ⋆s] L2 & + ∃∃I,L1,L2,V1,V2. L1 ⪤**[R, ⋆s] L2 & Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. #R #Y1 #Y2 #s #H elim H -Y2 [ #Y2 #H elim (lfxs_inv_sort … H) -H * @@ -107,9 +107,9 @@ lemma tc_lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⦻**[R, ⋆s] Y2 → ] qed-. -lemma tc_lfxs_inv_gref: ∀R,Y1,Y2,l. Y1 ⦻**[R, §l] Y2 → +lemma tc_lfxs_inv_gref: ∀R,Y1,Y2,l. Y1 ⪤**[R, §l] Y2 → (Y1 = ⋆ ∧ Y2 = ⋆) ∨ - ∃∃I,L1,L2,V1,V2. L1 ⦻**[R, §l] L2 & + ∃∃I,L1,L2,V1,V2. L1 ⪤**[R, §l] L2 & Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. #R #Y1 #Y2 #l #H elim H -Y2 [ #Y2 #H elim (lfxs_inv_gref … H) -H * @@ -126,16 +126,16 @@ lemma tc_lfxs_inv_gref: ∀R,Y1,Y2,l. Y1 ⦻**[R, §l] Y2 → qed-. lemma tc_lfxs_inv_bind: ∀R. (∀L. reflexive … (R L)) → - ∀p,I,L1,L2,V,T. L1 ⦻**[R, ⓑ{p,I}V.T] L2 → - L1 ⦻**[R, V] L2 ∧ L1.ⓑ{I}V ⦻**[R, T] L2.ⓑ{I}V. + ∀p,I,L1,L2,V,T. L1 ⪤**[R, ⓑ{p,I}V.T] L2 → + L1 ⪤**[R, V] L2 ∧ L1.ⓑ{I}V ⪤**[R, T] L2.ⓑ{I}V. #R #HR #p #I #L1 #L2 #V #T #H elim H -L2 [ #L2 #H elim (lfxs_inv_bind … V ? H) -H /3 width=1 by inj, conj/ | #L #L2 #_ #H * elim (lfxs_inv_bind … V ? H) -H /3 width=3 by tc_lfxs_step_dx, conj/ ] qed-. -lemma tc_lfxs_inv_flat: ∀R,I,L1,L2,V,T. L1 ⦻**[R, ⓕ{I}V.T] L2 → - L1 ⦻**[R, V] L2 ∧ L1 ⦻**[R, T] L2. +lemma tc_lfxs_inv_flat: ∀R,I,L1,L2,V,T. L1 ⪤**[R, ⓕ{I}V.T] L2 → + L1 ⪤**[R, V] L2 ∧ L1 ⪤**[R, T] L2. #R #I #L1 #L2 #V #T #H elim H -L2 [ #L2 #H elim (lfxs_inv_flat … H) -H /3 width=1 by inj, conj/ | #L #L2 #_ #H * elim (lfxs_inv_flat … H) -H /3 width=3 by tc_lfxs_step_dx, conj/ @@ -144,32 +144,32 @@ qed-. (* Advanced inversion lemmas ************************************************) -lemma tc_lfxs_inv_sort_pair_sn: ∀R,I,Y2,L1,V1,s. L1.ⓑ{I}V1 ⦻**[R, ⋆s] Y2 → - ∃∃L2,V2. L1 ⦻**[R, ⋆s] L2 & Y2 = L2.ⓑ{I}V2. +lemma tc_lfxs_inv_sort_pair_sn: ∀R,I,Y2,L1,V1,s. L1.ⓑ{I}V1 ⪤**[R, ⋆s] Y2 → + ∃∃L2,V2. L1 ⪤**[R, ⋆s] L2 & Y2 = L2.ⓑ{I}V2. #R #I #Y2 #L1 #V1 #s #H elim (tc_lfxs_inv_sort … H) -H * [ #H destruct | #J #Y1 #L2 #X1 #V2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/ ] qed-. -lemma tc_lfxs_inv_sort_pair_dx: ∀R,I,Y1,L2,V2,s. Y1 ⦻**[R, ⋆s] L2.ⓑ{I}V2 → - ∃∃L1,V1. L1 ⦻**[R, ⋆s] L2 & Y1 = L1.ⓑ{I}V1. +lemma tc_lfxs_inv_sort_pair_dx: ∀R,I,Y1,L2,V2,s. Y1 ⪤**[R, ⋆s] L2.ⓑ{I}V2 → + ∃∃L1,V1. L1 ⪤**[R, ⋆s] L2 & Y1 = L1.ⓑ{I}V1. #R #I #Y1 #L2 #V2 #s #H elim (tc_lfxs_inv_sort … H) -H * [ #_ #H destruct | #J #L1 #Y2 #V1 #X2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/ ] qed-. -lemma tc_lfxs_inv_gref_pair_sn: ∀R,I,Y2,L1,V1,l. L1.ⓑ{I}V1 ⦻**[R, §l] Y2 → - ∃∃L2,V2. L1 ⦻**[R, §l] L2 & Y2 = L2.ⓑ{I}V2. +lemma tc_lfxs_inv_gref_pair_sn: ∀R,I,Y2,L1,V1,l. L1.ⓑ{I}V1 ⪤**[R, §l] Y2 → + ∃∃L2,V2. L1 ⪤**[R, §l] L2 & Y2 = L2.ⓑ{I}V2. #R #I #Y2 #L1 #V1 #l #H elim (tc_lfxs_inv_gref … H) -H * [ #H destruct | #J #Y1 #L2 #X1 #V2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/ ] qed-. -lemma tc_lfxs_inv_gref_pair_dx: ∀R,I,Y1,L2,V2,l. Y1 ⦻**[R, §l] L2.ⓑ{I}V2 → - ∃∃L1,V1. L1 ⦻**[R, §l] L2 & Y1 = L1.ⓑ{I}V1. +lemma tc_lfxs_inv_gref_pair_dx: ∀R,I,Y1,L2,V2,l. Y1 ⪤**[R, §l] L2.ⓑ{I}V2 → + ∃∃L1,V1. L1 ⪤**[R, §l] L2 & Y1 = L1.ⓑ{I}V1. #R #I #Y1 #L2 #V2 #l #H elim (tc_lfxs_inv_gref … H) -H * [ #_ #H destruct | #J #L1 #Y2 #V1 #X2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/ @@ -178,18 +178,18 @@ qed-. (* Basic forward lemmas *****************************************************) -lemma tc_lfxs_fwd_pair_sn: ∀R,I,L1,L2,V,T. L1 ⦻**[R, ②{I}V.T] L2 → L1 ⦻**[R, V] L2. +lemma tc_lfxs_fwd_pair_sn: ∀R,I,L1,L2,V,T. L1 ⪤**[R, ②{I}V.T] L2 → L1 ⪤**[R, V] L2. #R #I #L1 #L2 #V #T #H elim H -L2 /3 width=5 by lfxs_fwd_pair_sn, tc_lfxs_step_dx, inj/ qed-. lemma tc_lfxs_fwd_bind_dx: ∀R. (∀L. reflexive … (R L)) → - ∀p,I,L1,L2,V,T. L1 ⦻**[R, ⓑ{p,I}V.T] L2 → - L1.ⓑ{I}V ⦻**[R, T] L2.ⓑ{I}V. + ∀p,I,L1,L2,V,T. L1 ⪤**[R, ⓑ{p,I}V.T] L2 → + L1.ⓑ{I}V ⪤**[R, T] L2.ⓑ{I}V. #R #HR #p #I #L1 #L2 #V #T #H elim (tc_lfxs_inv_bind … H) -H // qed-. -lemma tc_lfxs_fwd_flat_dx: ∀R,I,L1,L2,V,T. L1 ⦻**[R, ⓕ{I}V.T] L2 → L1 ⦻**[R, T] L2. +lemma tc_lfxs_fwd_flat_dx: ∀R,I,L1,L2,V,T. L1 ⪤**[R, ⓕ{I}V.T] L2 → L1 ⪤**[R, T] L2. #R #I #L1 #L2 #V #T #H elim (tc_lfxs_inv_flat … H) -H // qed-.