From 0098ddc7269a3fc4a554cf386d2a234d61d53d44 Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Tue, 17 Oct 2017 15:24:43 +0000 Subject: [PATCH] - exclusion binder in local environments component i_static updated (this is part of last milestone) --- .../lambdadelta/basic_2/etc/tc_lfxs.etc | 15 ++++ .../lambdadelta/basic_2/i_static/tc_lfxs.ma | 74 ++++++++++--------- .../basic_2/i_static/tc_lfxs_fqup.ma | 19 +++++ .../basic_2/i_static/tc_lfxs_tc_lfxs.ma | 2 +- .../lambdadelta/basic_2/web/basic_2.ldw.xml | 5 +- .../lambdadelta/basic_2/web/basic_2_src.tbl | 2 +- 6 files changed, 78 insertions(+), 39 deletions(-) diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/tc_lfxs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/tc_lfxs.etc index e2f613a87..8e7e11183 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/etc/tc_lfxs.etc +++ b/matita/matita/contribs/lambdadelta/basic_2/etc/tc_lfxs.etc @@ -39,6 +39,21 @@ axiom s_r_conf2_LTC2: ∀R. s_r_transitive … R (lfxs R) → #L1 #L #HL1 #HL2 #IH @(tc_lfxs_step_sn … IH) -IH // *) +lemma tc_lfxs_inv_zero: ∀R,Y1,Y2. Y1 ⪤**[R, #0] Y2 → + ∨∨ Y1 = ⋆ ∧ Y2 = ⋆ + | ∃∃I,L1,L2,V1,V2. L1 ⪤**[R, V1] L2 & R L1 V1 V2 & + Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2 + | ∃∃f,I,L1,L2. 𝐈⦃f⦄ & L1 ⪤*[cext2 R, cfull, f] L2 & + Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}. +#R #Y1 #Y2 #H elim H -Y2 +[ +| #Y #Y2 #_ #H elim (lfxs_inv_zero … H) -H * + [ #H #H2 * * /3 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex4_4_intro, conj/ + | #I #L #L2 #V #V2 #HL2 #HV2 #H #H2 * * + [ #H1 #H0 destruct + | #I0 #L0 #L1 #V0 #V1 #HL01 #HV01 #H1 #H0 destruct + + lemma tc_lfxs_inv_zero: ∀R. s_r_confluent1 … R (lfxs R) → s_r_transitive … R (lfxs R) → ∀Y1,Y2. Y1 ⦻**[R, #0] Y2 → 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 e1dd22673..8e3bf8a4d 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 @@ -44,13 +44,17 @@ lemma tc_lfxs_sort: ∀R,I,L1,L2,V1,V2,s. /3 width=4 by lfxs_sort, tc_lfxs_step_dx, inj/ qed. -lemma tc_lfxs_zero: ∀R. (∀L. reflexive … (R L)) → +lemma tc_lfxs_pair: ∀R. (∀L. reflexive … (R L)) → ∀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/ +/3 width=5 by lfxs_pair, tc_lfxs_step_dx, inj/ qed. +lemma tc_lfxs_unit: ∀R,f,I,L1,L2. 𝐈⦃f⦄ → L1 ⪤*[cext2 R, cfull, f] L2 → + L1.ⓤ{I} ⪤**[R, #0] L2.ⓤ{I}. +/3 width=3 by lfxs_unit, 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. #R #I #L1 #L2 #V1 #V2 #i #H elim H -L2 @@ -63,7 +67,7 @@ lemma tc_lfxs_gref: ∀R,I,L1,L2,V1,V2,l. /3 width=4 by lfxs_gref, tc_lfxs_step_dx, inj/ qed. -lemma tc_lfxs_sym: ∀R. lexs_frees_confluent R cfull → +lemma tc_lfxs_sym: ∀R. lexs_frees_confluent (cext2 R) cfull → (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) → ∀T. symmetric … (tc_lfxs R T). #R #H1R #H2R #T #L1 #L2 #H elim H -L2 @@ -90,36 +94,36 @@ lemma tc_lfxs_inv_atom_dx: ∀R,I,Y1. Y1 ⪤**[R, ⓪{I}] ⋆ → Y1 = ⋆. qed-. lemma tc_lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⪤**[R, ⋆s] Y2 → - (Y1 = ⋆ ∧ Y2 = ⋆) ∨ - ∃∃I,L1,L2,V1,V2. L1 ⪤**[R, ⋆s] L2 & - Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. + ∨∨ Y1 = ⋆ ∧ Y2 = ⋆ + | ∃∃I1,I2,L1,L2. L1 ⪤**[R, ⋆s] L2 & + Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}. #R #Y1 #Y2 #s #H elim H -Y2 [ #Y2 #H elim (lfxs_inv_sort … H) -H * - /4 width=8 by ex3_5_intro, inj, or_introl, or_intror, conj/ + /4 width=8 by ex3_4_intro, inj, or_introl, or_intror, conj/ | #Y #Y2 #_ #H elim (lfxs_inv_sort … H) -H * - [ #H #H2 * * /3 width=8 by ex3_5_intro, or_introl, or_intror, conj/ - | #I #L #L2 #V #V2 #HL2 #H #H2 * * + [ #H #H2 * * /3 width=7 by ex3_4_intro, or_introl, or_intror, conj/ + | #I #I2 #L #L2 #HL2 #H #H2 * * [ #H1 #H0 destruct - | #I0 #L1 #L0 #V1 #V0 #HL10 #H1 #H0 destruct - /4 width=8 by ex3_5_intro, tc_lfxs_step_dx, or_intror/ + | #I1 #I0 #L1 #L0 #HL10 #H1 #H0 destruct + /4 width=7 by ex3_4_intro, tc_lfxs_step_dx, or_intror/ ] ] ] qed-. lemma tc_lfxs_inv_gref: ∀R,Y1,Y2,l. Y1 ⪤**[R, §l] Y2 → - (Y1 = ⋆ ∧ Y2 = ⋆) ∨ - ∃∃I,L1,L2,V1,V2. L1 ⪤**[R, §l] L2 & - Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. + ∨∨ Y1 = ⋆ ∧ Y2 = ⋆ + | ∃∃I1,I2,L1,L2. L1 ⪤**[R, §l] L2 & + Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}. #R #Y1 #Y2 #l #H elim H -Y2 [ #Y2 #H elim (lfxs_inv_gref … H) -H * - /4 width=8 by ex3_5_intro, inj, or_introl, or_intror, conj/ + /4 width=8 by ex3_4_intro, inj, or_introl, or_intror, conj/ | #Y #Y2 #_ #H elim (lfxs_inv_gref … H) -H * - [ #H #H2 * * /3 width=8 by ex3_5_intro, or_introl, or_intror, conj/ - | #I #L #L2 #V #V2 #HL2 #H #H2 * * + [ #H #H2 * * /3 width=7 by ex3_4_intro, or_introl, or_intror, conj/ + | #I #I2 #L #L2 #HL2 #H #H2 * * [ #H1 #H0 destruct - | #I0 #L1 #L0 #V1 #V0 #HL10 #H1 #H0 destruct - /4 width=8 by ex3_5_intro, tc_lfxs_step_dx, or_intror/ + | #I1 #I0 #L1 #L0 #HL10 #H1 #H0 destruct + /4 width=7 by ex3_4_intro, tc_lfxs_step_dx, or_intror/ ] ] ] @@ -144,35 +148,35 @@ 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. -#R #I #Y2 #L1 #V1 #s #H elim (tc_lfxs_inv_sort … H) -H * +lemma tc_lfxs_inv_sort_bind_sn: ∀R,I1,Y2,L1,s. L1.ⓘ{I1} ⪤**[R, ⋆s] Y2 → + ∃∃I2,L2. L1 ⪤**[R, ⋆s] L2 & Y2 = L2.ⓘ{I2}. +#R #I1 #Y2 #L1 #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/ +| #Z #I2 #Y1 #L2 #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. -#R #I #Y1 #L2 #V2 #s #H elim (tc_lfxs_inv_sort … H) -H * +lemma tc_lfxs_inv_sort_bind_dx: ∀R,I2,Y1,L2,s. Y1 ⪤**[R, ⋆s] L2.ⓘ{I2} → + ∃∃I1,L1. L1 ⪤**[R, ⋆s] L2 & Y1 = L1.ⓘ{I1}. +#R #I2 #Y1 #L2 #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/ +| #I1 #Z #L1 #Y2 #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. -#R #I #Y2 #L1 #V1 #l #H elim (tc_lfxs_inv_gref … H) -H * +lemma tc_lfxs_inv_gref_bind_sn: ∀R,I1,Y2,L1,l. L1.ⓘ{I1} ⪤**[R, §l] Y2 → + ∃∃I2,L2. L1 ⪤**[R, §l] L2 & Y2 = L2.ⓘ{I2}. +#R #I1 #Y2 #L1 #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/ +| #Z #I2 #Y1 #L2 #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. -#R #I #Y1 #L2 #V2 #l #H elim (tc_lfxs_inv_gref … H) -H * +lemma tc_lfxs_inv_gref_bind_dx: ∀R,I2,Y1,L2,l. Y1 ⪤**[R, §l] L2.ⓘ{I2} → + ∃∃I1,L1. L1 ⪤**[R, §l] L2 & Y1 = L1.ⓘ{I1}. +#R #I2 #Y1 #L2 #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/ +| #I1 #Z #L1 #Y2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/ ] qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma index e69f071f2..ce56a3154 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma @@ -46,3 +46,22 @@ lemma tc_lfxs_ind_dx: ∀R. (∀L. reflexive … (R L)) → #R #HR #L2 #R0 #HL2 #IHL2 #L1 #HL12 @(TC_star_ind_dx … HL2 IHL2 … HL12) /2 width=4 by lfxs_refl/ qed-. + +(* Advanced inversion lemmas ************************************************) + +lemma tc_lfxs_inv_bind_void: ∀R. (∀L. reflexive … (R L)) → + ∀p,I,L1,L2,V,T. L1 ⪤**[R, ⓑ{p,I}V.T] L2 → + L1 ⪤**[R, V] L2 ∧ L1.ⓧ ⪤**[R, T] L2.ⓧ. +#R #HR #p #I #L1 #L2 #V #T #H @(tc_lfxs_ind_sn … HR … H) -L2 +[ /3 width=1 by tc_lfxs_refl, conj/ +| #L #L2 #_ #H * elim (lfxs_inv_bind_void … H) -H /3 width=3 by tc_lfxs_step_dx, conj/ +] +qed-. + +(* Advanced forward lemmas **************************************************) + +lemma tc_lfxs_fwd_bind_dx_void: ∀R. (∀L. reflexive … (R L)) → + ∀p,I,L1,L2,V,T. L1 ⪤**[R, ⓑ{p,I}V.T] L2 → + L1.ⓧ ⪤**[R, T] L2.ⓧ. +#R #HR #p #I #L1 #L2 #V #T #H elim (tc_lfxs_inv_bind_void … H) -H // +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_tc_lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_tc_lfxs.ma index 4fe37f452..62173d926 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_tc_lfxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_tc_lfxs.ma @@ -19,5 +19,5 @@ include "basic_2/i_static/tc_lfxs.ma". (* Main properties **********************************************************) theorem tc_lfxs_trans: ∀R,T. Transitive … (tc_lfxs R T). -#R #T #L1 #L #HL1 #L2 #HL2 @(trans_TC … HL1 HL2) (**) (* auto fails *) +#R #T #L1 #L #HL1 #L2 #HL2 @(trans_TC … HL1 HL2) (**) (* auto fails *) qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml index 74819fc02..dcf2f4693 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml +++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml @@ -34,9 +34,10 @@ Stage "A2": "Extending the Applicability Condition" - + Exclusion binder in local environments. - Ported components: syntax, relocation, s_transition, s_computation, static. + Syntactic component updated: + syntax, relocation, s_transition, s_computation, static, i_static. Strong rt-normalization diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl index 059745fe9..df82586f0 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl +++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl @@ -148,6 +148,7 @@ table { ] } ] +*) class "water" [ { "iterated static typing" * } { [ { "iterated extension on referred entries" * } { @@ -156,7 +157,6 @@ table { ] } ] -*) class "green" [ { "static typing" * } { [ { "generic reducibility" * } { -- 2.39.2