From 4ce795bb1d356e2565c14087b933adaccfc81dcd Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Tue, 17 Oct 2017 18:31:39 +0000 Subject: [PATCH] - exclusion binder in local environments updating of component rt_transition started cpg completed --- .../lambdadelta/basic_2/rt_transition/cpg.ma | 36 +++++++------- .../basic_2/rt_transition/cpg_drops.ma | 48 +++++++++++-------- .../basic_2/rt_transition/cpg_lsubr.ma | 8 ++-- .../lambdadelta/basic_2/syntax/tdeq_ext.ma | 7 ++- .../lambdadelta/basic_2/web/basic_2_src.tbl | 8 ++-- 5 files changed, 59 insertions(+), 48 deletions(-) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma index b682e561d..260cd45a4 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma @@ -30,8 +30,8 @@ inductive cpg (Rt:relation rtc) (h): rtc → relation4 genv lenv term term ≝ ⬆*[1] V2 ≡ W2 → cpg Rt h c G (L.ⓓV1) (#0) W2 | cpg_ell : ∀c,G,L,V1,V2,W2. cpg Rt h c G L V1 V2 → ⬆*[1] V2 ≡ W2 → cpg Rt h (c+𝟘𝟙) G (L.ⓛV1) (#0) W2 -| cpg_lref : ∀c,I,G,L,V,T,U,i. cpg Rt h c G L (#i) T → - ⬆*[1] T ≡ U → cpg Rt h c G (L.ⓑ{I}V) (#⫯i) U +| cpg_lref : ∀c,I,G,L,T,U,i. cpg Rt h c G L (#i) T → + ⬆*[1] T ≡ U → cpg Rt h c G (L.ⓘ{I}) (#⫯i) U | cpg_bind : ∀cV,cT,p,I,G,L,V1,V2,T1,T2. cpg Rt h cV G L V1 V2 → cpg Rt h cT G (L.ⓑ{I}V1) T1 T2 → cpg Rt h ((↓cV)∨cT) G L (ⓑ{p,I}V1.T1) (ⓑ{p,I}V2.T2) @@ -75,14 +75,14 @@ fact cpg_inv_atom1_aux: ∀Rt,c,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈[Rt, c, h] T2 L = K.ⓓV1 & J = LRef 0 & c = cV | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈[Rt, cV, h] V2 & ⬆*[1] V2 ≡ T2 & L = K.ⓛV1 & J = LRef 0 & c = cV+𝟘𝟙 - | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 & - L = K.ⓑ{I}V & J = LRef (⫯i). + | ∃∃I,K,T,i. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 & + L = K.ⓘ{I} & J = LRef (⫯i). #Rt #c #h #G #L #T1 #T2 * -c -G -L -T1 -T2 [ #I #G #L #J #H destruct /3 width=1 by or5_intro0, conj/ | #G #L #s #J #H destruct /3 width=3 by or5_intro1, ex3_intro/ | #c #G #L #V1 #V2 #W2 #HV12 #VW2 #J #H destruct /3 width=8 by or5_intro2, ex5_4_intro/ | #c #G #L #V1 #V2 #W2 #HV12 #VW2 #J #H destruct /3 width=8 by or5_intro3, ex5_4_intro/ -| #c #I #G #L #V #T #U #i #HT #HTU #J #H destruct /3 width=9 by or5_intro4, ex4_5_intro/ +| #c #I #G #L #T #U #i #HT #HTU #J #H destruct /3 width=8 by or5_intro4, ex4_4_intro/ | #cV #cT #p #I #G #L #V1 #V2 #T1 #T2 #_ #_ #J #H destruct | #cV #cT #G #L #V1 #V2 #T1 #T2 #_ #_ #J #H destruct | #cU #cT #G #L #U1 #U2 #T1 #T2 #_ #_ #_ #J #H destruct @@ -101,8 +101,8 @@ lemma cpg_inv_atom1: ∀Rt,c,h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ⬈[Rt, c, h] T2 L = K.ⓓV1 & J = LRef 0 & c = cV | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈[Rt, cV, h] V2 & ⬆*[1] V2 ≡ T2 & L = K.ⓛV1 & J = LRef 0 & c = cV+𝟘𝟙 - | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 & - L = K.ⓑ{I}V & J = LRef (⫯i). + | ∃∃I,K,T,i. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 & + L = K.ⓘ{I} & J = LRef (⫯i). /2 width=3 by cpg_inv_atom1_aux/ qed-. lemma cpg_inv_sort1: ∀Rt,c,h,G,L,T2,s. ⦃G, L⦄ ⊢ ⋆s ⬈[Rt, c, h] T2 → @@ -111,7 +111,7 @@ lemma cpg_inv_sort1: ∀Rt,c,h,G,L,T2,s. ⦃G, L⦄ ⊢ ⋆s ⬈[Rt, c, h] T2 elim (cpg_inv_atom1 … H) -H * /3 width=1 by or_introl, conj/ [ #s0 #H destruct /3 width=1 by or_intror, conj/ |2,3: #cV #K #V1 #V2 #_ #_ #_ #H destruct -| #I #K #V1 #V2 #i #_ #_ #_ #H destruct +| #I #K #T #i #_ #_ #_ #H destruct ] qed-. @@ -125,18 +125,18 @@ lemma cpg_inv_zero1: ∀Rt,c,h,G,L,T2. ⦃G, L⦄ ⊢ #0 ⬈[Rt, c, h] T2 → elim (cpg_inv_atom1 … H) -H * /3 width=1 by or3_intro0, conj/ [ #s #H destruct |2,3: #cV #K #V1 #V2 #HV12 #HVT2 #H1 #_ #H2 destruct /3 width=8 by or3_intro1, or3_intro2, ex4_4_intro/ -| #I #K #V1 #V2 #i #_ #_ #_ #H destruct +| #I #K #T #i #_ #_ #_ #H destruct ] qed-. lemma cpg_inv_lref1: ∀Rt,c,h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ⬈[Rt, c, h] T2 → (T2 = #(⫯i) ∧ c = 𝟘𝟘) ∨ - ∃∃I,K,V,T. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V. + ∃∃I,K,T. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 & L = K.ⓘ{I}. #Rt #c #h #G #L #T2 #i #H elim (cpg_inv_atom1 … H) -H * /3 width=1 by or_introl, conj/ [ #s #H destruct |2,3: #cV #K #V1 #V2 #_ #_ #_ #H destruct -| #I #K #V1 #V2 #j #HV2 #HVT2 #H1 #H2 destruct /3 width=7 by ex3_4_intro, or_intror/ +| #I #K #T #j #HT #HT2 #H1 #H2 destruct /3 width=6 by ex3_3_intro, or_intror/ ] qed-. @@ -145,7 +145,7 @@ lemma cpg_inv_gref1: ∀Rt,c,h,G,L,T2,l. ⦃G, L⦄ ⊢ §l ⬈[Rt, c, h] T2 → elim (cpg_inv_atom1 … H) -H * /2 width=1 by conj/ [ #s #H destruct |2,3: #cV #K #V1 #V2 #_ #_ #_ #H destruct -| #I #K #V1 #V2 #i #_ #_ #_ #H destruct +| #I #K #T #i #_ #_ #_ #H destruct ] qed-. @@ -161,7 +161,7 @@ fact cpg_inv_bind1_aux: ∀Rt,c,h,G,L,U,U2. ⦃G, L⦄ ⊢ U ⬈[Rt, c, h] U2 | #G #L #s #q #J #W #U1 #H destruct | #c #G #L #V1 #V2 #W2 #_ #_ #q #J #W #U1 #H destruct | #c #G #L #V1 #V2 #W2 #_ #_ #q #J #W #U1 #H destruct -| #c #I #G #L #V #T #U #i #_ #_ #q #J #W #U1 #H destruct +| #c #I #G #L #T #U #i #_ #_ #q #J #W #U1 #H destruct | #cV #cT #p #I #G #L #V1 #V2 #T1 #T2 #HV12 #HT12 #q #J #W #U1 #H destruct /3 width=8 by ex4_4_intro, or_introl/ | #cV #cT #G #L #V1 #V2 #T1 #T2 #_ #_ #q #J #W #U1 #H destruct | #cU #cT #G #L #U1 #U2 #T1 #T2 #_ #_ #_ #q #J #W #U1 #H destruct @@ -213,7 +213,7 @@ fact cpg_inv_appl1_aux: ∀Rt,c,h,G,L,U,U2. ⦃G, L⦄ ⊢ U ⬈[Rt, c, h] U2 | #G #L #s #W #U1 #H destruct | #c #G #L #V1 #V2 #W2 #_ #_ #W #U1 #H destruct | #c #G #L #V1 #V2 #W2 #_ #_ #W #U1 #H destruct -| #c #I #G #L #V #T #U #i #_ #_ #W #U1 #H destruct +| #c #I #G #L #T #U #i #_ #_ #W #U1 #H destruct | #cV #cT #p #I #G #L #V1 #V2 #T1 #T2 #_ #_ #W #U1 #H destruct | #cV #cT #G #L #V1 #V2 #T1 #T2 #HV12 #HT12 #W #U1 #H destruct /3 width=8 by or3_intro0, ex4_4_intro/ | #cV #cT #G #L #V1 #V2 #T1 #T2 #_ #_ #_ #W #U1 #H destruct @@ -245,7 +245,7 @@ fact cpg_inv_cast1_aux: ∀Rt,c,h,G,L,U,U2. ⦃G, L⦄ ⊢ U ⬈[Rt, c, h] U2 | #G #L #s #W #U1 #H destruct | #c #G #L #V1 #V2 #W2 #_ #_ #W #U1 #H destruct | #c #G #L #V1 #V2 #W2 #_ #_ #W #U1 #H destruct -| #c #I #G #L #V #T #U #i #_ #_ #W #U1 #H destruct +| #c #I #G #L #T #U #i #_ #_ #W #U1 #H destruct | #cV #cT #p #I #G #L #V1 #V2 #T1 #T2 #_ #_ #W #U1 #H destruct | #cV #cT #G #L #V1 #V2 #T1 #T2 #_ #_ #W #U1 #H destruct | #cV #cT #G #L #V1 #V2 #T1 #T2 #HRt #HV12 #HT12 #W #U1 #H destruct /3 width=9 by or3_intro0, ex5_4_intro/ @@ -276,11 +276,11 @@ lemma cpg_inv_zero1_pair: ∀Rt,c,h,I,G,K,V1,T2. ⦃G, K.ⓑ{I}V1⦄ ⊢ #0 ⬈[ * #z #Y #X1 #X2 #HX12 #HXT2 #H1 #H2 destruct /3 width=5 by or3_intro1, or3_intro2, ex4_2_intro/ qed-. -lemma cpg_inv_lref1_pair: ∀Rt,c,h,I,G,K,V,T2,i. ⦃G, K.ⓑ{I}V⦄ ⊢ #⫯i ⬈[Rt, c, h] T2 → +lemma cpg_inv_lref1_bind: ∀Rt,c,h,I,G,K,T2,i. ⦃G, K.ⓘ{I}⦄ ⊢ #⫯i ⬈[Rt, c, h] T2 → (T2 = #(⫯i) ∧ c = 𝟘𝟘) ∨ ∃∃T. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2. -#Rt #c #h #I #G #L #V #T2 #i #H elim (cpg_inv_lref1 … H) -H /2 width=1 by or_introl/ -* #Z #Y #X #T #HT #HT2 #H destruct /3 width=3 by ex2_intro, or_intror/ +#Rt #c #h #I #G #L #T2 #i #H elim (cpg_inv_lref1 … H) -H /2 width=1 by or_introl/ +* #Z #Y #T #HT #HT2 #H destruct /3 width=3 by ex2_intro, or_intror/ qed-. (* Basic forward lemmas *****************************************************) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma index 758a278b7..295cc2291 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma @@ -26,7 +26,7 @@ lemma cpg_delta_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≡ K.ⓓV → ⦃G, #Rt #c #h #G #K #V #V2 #i elim i -i [ #L #T2 #HLK lapply (drops_fwd_isid … HLK ?) // #H destruct /3 width=3 by cpg_delta/ | #i #IH #L0 #T0 #H0 #HV2 #HVT2 - elim (drops_inv_succ … H0) -H0 #I #L #V0 #HLK #H destruct + elim (drops_inv_succ … H0) -H0 #I #L #HLK #H destruct elim (lifts_split_trans … HVT2 (𝐔❴⫯i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/ ] qed. @@ -36,7 +36,7 @@ lemma cpg_ell_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≡ K.ⓛV → ⦃G, K #Rt #c #h #G #K #V #V2 #i elim i -i [ #L #T2 #HLK lapply (drops_fwd_isid … HLK ?) // #H destruct /3 width=3 by cpg_ell/ | #i #IH #L0 #T0 #H0 #HV2 #HVT2 - elim (drops_inv_succ … H0) -H0 #I #L #V0 #HLK #H destruct + elim (drops_inv_succ … H0) -H0 #I #L #HLK #H destruct elim (lifts_split_trans … HVT2 (𝐔❴⫯i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/ ] qed. @@ -53,7 +53,7 @@ lemma cpg_inv_lref1_drops: ∀Rt,c,h,G,i,L,T2. ⦃G, L⦄ ⊢ #i ⬈[Rt,c, h] T2 [ #L #T2 #H elim (cpg_inv_zero1 … H) -H * /3 width=1 by or3_intro0, conj/ /4 width=8 by drops_refl, ex4_4_intro, or3_intro2, or3_intro1/ | #i #IH #L #T2 #H elim (cpg_inv_lref1 … H) -H * /3 width=1 by or3_intro0, conj/ - #I #K #V #V2 #H #HVT2 #H0 destruct elim (IH … H) -IH -H + #I #K #V2 #H #HVT2 #H0 destruct elim (IH … H) -IH -H [ * #H1 #H2 destruct lapply (lifts_inv_lref1_uni … HVT2) -HVT2 #H destruct /3 width=1 by or3_intro0, conj/ ] * #cV #L #W #W2 #HKL #HW2 #HWV2 #H destruct lapply (lifts_trans … HWV2 … HVT2 ??) -V2 @@ -81,9 +81,10 @@ qed-. (* Properties with generic slicing for local environments *******************) (* Note: it should use drops_split_trans_pair2 *) -lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt h c G). +lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → + ∀c,h,G. d_liftable2_sn … lifts (cpg Rt h c G). #Rt #HRt #c #h #G #K #T generalize in match c; -c -@(fqup_wf_ind_eq … G K T) -G -K -T #G0 #K0 #T0 #IH #G #K * * +@(fqup_wf_ind_eq (Ⓣ) … G K T) -G -K -T #G0 #K0 #T0 #IH #G #K * * [ #s #HG #HK #HT #c #X2 #H2 #b #f #L #HLK #X1 #H1 destruct -IH lapply (lifts_inv_sort1 … H1) -H1 #H destruct elim (cpg_inv_sort1 … H2) -H2 * #H1 #H2 destruct @@ -96,7 +97,8 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt lapply (drops_trans … HLK … HK0 ??) -HLK [3,6: |*: // ] #H elim (drops_split_trans … H) -H [1,6: |*: /2 width=6 by after_uni_dx/ ] #Y #HL0 #HY lapply (drops_tls_at … Hf … HY) -HY #HY - elim (drops_inv_skip2 … HY) -HY #L0 #W #HLK0 #HVW #H destruct + elim (drops_inv_skip2 … HY) -HY #Z #L0 #HLK0 #HZ #H destruct + elim (liftsb_inv_pair_sn … HZ) -HZ #W #HVW #H destruct elim (IH … HV2 … HLK0 … HVW) -IH /2 width=2 by fqup_lref/ -K -K0 -V #W2 #HVW2 #HW2 elim (lifts_total W2 (𝐔❴⫯i2❵)) #U2 #HWU2 lapply (lifts_trans … HVW2 … HWU2 ??) -HVW2 [3,6: |*: // ] #HVU2 @@ -111,10 +113,10 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt elim (cpg_inv_bind1 … H2) -H2 * [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct elim (IH … HV12 … HLK … HVW1) -HV12 // - elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] + elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] /3 width=5 by cpg_bind, lifts_bind, ex2_intro/ | #cT #T2 #HT12 #HXT2 #H1 #H2 #H3 destruct - elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] #U2 #HTU2 #HU12 + elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] #U2 #HTU2 #HU12 lapply (lifts_trans … HXT2 … HTU2 ??) -T2 [3: |*: // ] #HXU2 elim (lifts_split_trans … HXU2 f (𝐔❴⫯O❵)) [2: /2 width=1 by after_uni_one_dx/ ] /3 width=5 by cpg_zeta, ex2_intro/ @@ -130,13 +132,13 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt elim (lifts_inv_bind1 … HTU1) -HTU1 #Z1 #U0 #HYZ1 #HTU1 #H destruct elim (IH … HV12 … HLK … HVW1) -HV12 -HVW1 // elim (IH … HY12 … HLK … HYZ1) -HY12 // - elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] + elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] /4 width=7 by cpg_beta, lifts_bind, lifts_flat, ex2_intro/ | #cV #cY #cT #a #V2 #V20 #Y1 #Y2 #T0 #T2 #HV12 #HV20 #HY12 #HT12 #H1 #H2 #H3 destruct elim (lifts_inv_bind1 … HTU1) -HTU1 #Z1 #U0 #HYZ1 #HTU1 #H destruct elim (IH … HV12 … HLK … HVW1) -HV12 -HVW1 // #W2 #HVW2 #HW12 elim (IH … HY12 … HLK … HYZ1) -HY12 // - elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] + elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] elim (lifts_total W2 (𝐔❴1❵)) #W20 #HW20 lapply (lifts_trans … HVW2 … HW20 ??) -HVW2 [3: |*: // ] #H lapply (lifts_conf … HV20 … H (↑f) ?) -V2 /2 width=3 by after_uni_one_sn/ @@ -158,14 +160,16 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt ] qed-. -lemma cpg_lifts_bi: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_bi (cpg Rt h c G). -/3 width=9 by cpg_lifts_sn, d_liftable2_sn_bi/ qed-. +lemma cpg_lifts_bi: ∀Rt. reflexive … Rt → + ∀c,h,G. d_liftable2_bi … lifts (cpg Rt h c G). +/3 width=12 by cpg_lifts_sn, d_liftable2_sn_bi, lifts_mono/ qed-. (* Inversion lemmas with generic slicing for local environments *************) -lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn (cpg Rt h c G). +lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → + ∀c,h,G. d_deliftable2_sn … lifts (cpg Rt h c G). #Rt #HRt #c #h #G #L #U generalize in match c; -c -@(fqup_wf_ind_eq … G L U) -G -L -U #G0 #L0 #U0 #IH #G #L * * +@(fqup_wf_ind_eq (Ⓣ) … G L U) -G -L -U #G0 #L0 #U0 #IH #G #L * * [ #s #HG #HL #HU #c #X2 #H2 #b #f #K #HLK #X1 #H1 destruct -IH lapply (lifts_inv_sort2 … H1) -H1 #H destruct elim (cpg_inv_sort1 … H2) -H2 * #H1 #H2 destruct @@ -178,7 +182,8 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn ( lapply (drops_split_div … HLK (𝐔❴i1❵) ???) -HLK [4,8: * |*: // ] #Y0 #HK0 #HLY0 lapply (drops_conf … HL0 … HLY0 ??) -HLY0 [3,6: |*: /2 width=6 by after_uni_dx/ ] #HLY0 lapply (drops_tls_at … Hf … HLY0) -HLY0 #HLY0 - elim (drops_inv_skip1 … HLY0) -HLY0 #K0 #V #HLK0 #HVW #H destruct + elim (drops_inv_skip1 … HLY0) -HLY0 #Z #K0 #HLK0 #HZ #H destruct + elim (liftsb_inv_pair_dx … HZ) -HZ #V #HVW #H destruct elim (IH … HW2 … HLK0 … HVW) -IH /2 width=2 by fqup_lref/ -L -L0 -W #V2 #HVW2 #HV2 lapply (lifts_trans … HVW2 … HWU2 ??) -W2 [3,6: |*: // ] #HVU2 elim (lifts_split_trans … HVU2 ? f) -HVU2 [1,4: |*: /2 width=4 by after_uni_succ_sn/ ] @@ -192,10 +197,10 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn ( elim (cpg_inv_bind1 … H2) -H2 * [ #cW #cU #W2 #U2 #HW12 #HU12 #H1 #H2 destruct elim (IH … HW12 … HLK … HVW1) -HW12 // - elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] + elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] /3 width=5 by cpg_bind, lifts_bind, ex2_intro/ | #cU #U2 #HU12 #HXU2 #H1 #H2 #H3 destruct - elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] #T2 #HTU2 #HT12 + elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] #T2 #HTU2 #HT12 elim (lifts_div4_one … HTU2 … HXU2) -U2 /3 width=5 by cpg_zeta, ex2_intro/ ] | * #W1 #U1 #HG #HL #HU #c #X2 #H2 #b #f #K #HLK #X1 #H1 destruct @@ -209,13 +214,13 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn ( elim (lifts_inv_bind2 … HTU1) -HTU1 #Y1 #T0 #HYZ1 #HTU1 #H destruct elim (IH … HW12 … HLK … HVW1) -HW12 -HVW1 // elim (IH … HZ12 … HLK … HYZ1) -HZ12 // - elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] + elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] /4 width=7 by cpg_beta, lifts_bind, lifts_flat, ex2_intro/ | #cW #cZ #cU #a #W2 #W20 #Z1 #Z2 #U0 #U2 #HW12 #HW20 #HZ12 #HU12 #H1 #H2 #H3 destruct elim (lifts_inv_bind2 … HTU1) -HTU1 #Y1 #T0 #HYZ1 #HTU1 #H destruct elim (IH … HW12 … HLK … HVW1) -HW12 -HVW1 // #V2 #HVW2 #HV12 elim (IH … HZ12 … HLK … HYZ1) -HZ12 // - elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] + elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] lapply (lifts_trans … HVW2 … HW20 ??) -W2 [3: |*: // ] #H elim (lifts_split_trans … H ? (↑f)) -H [ |*: /2 width=3 by after_uni_one_sn/ ] /4 width=9 by cpg_theta, lifts_bind, lifts_flat, ex2_intro/ @@ -236,5 +241,6 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn ( ] qed-. -lemma cpg_inv_lifts_bi: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_bi (cpg Rt h c G). -/3 width=9 by cpg_inv_lifts_sn, d_deliftable2_sn_bi/ qed-. +lemma cpg_inv_lifts_bi: ∀Rt. reflexive … Rt → + ∀c,h,G. d_deliftable2_bi … lifts (cpg Rt h c G). +/3 width=12 by cpg_inv_lifts_sn, d_deliftable2_sn_bi, lifts_inj/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma index 8dcc523e4..77425cce7 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma @@ -29,11 +29,11 @@ lemma lsubr_cpg_trans: ∀Rt,c,h,G. lsub_trans … (cpg Rt h c G) lsubr. | #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H elim (lsubr_inv_abst2 … H) -H * #L2 [2: #V ] #HL21 #H destruct /4 width=3 by cpg_delta, cpg_ell, cpg_ee/ -| #c #I1 #G #L1 #V1 #T1 #U1 #i #_ #HTU1 #IH #X #H - elim (lsubr_fwd_pair2 … H) -H #I2 #L2 #V2 #HL21 #H destruct +| #c #I1 #G #L1 #T1 #U1 #i #_ #HTU1 #IH #X #H + elim (lsubr_fwd_bind2 … H) -H #I2 #L2 #HL21 #H destruct /3 width=3 by cpg_lref/ -|6,12: /4 width=1 by cpg_bind, cpg_beta, lsubr_pair/ +|6,12: /4 width=1 by cpg_bind, cpg_beta, lsubr_bind/ |7,8,10,11: /3 width=1 by cpg_appl, cpg_cast, cpg_eps, cpg_ee/ -|9,13: /4 width=3 by cpg_zeta, cpg_theta, lsubr_pair/ +|9,13: /4 width=3 by cpg_zeta, cpg_theta, lsubr_bind/ ] qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_ext.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_ext.ma index 4783017ee..c4ed53ed0 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_ext.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_ext.ma @@ -20,9 +20,12 @@ include "basic_2/syntax/lenv_ext2.ma". definition cdeq: ∀h. sd h → relation3 lenv term term ≝ λh,o,L. tdeq h o. +definition tdeq_ext: ∀h. sd h → relation bind ≝ + λh,o. ext2 (tdeq h o). + definition cdeq_ext: ∀h. sd h → relation3 lenv bind bind ≝ λh,o. cext2 (cdeq h o). interpretation - "degree-based equivalence (binders)" - 'LazyEq h o I1 I2 = (ext2 (tdeq h o) I1 I2). + "degree-based equivalence (binder)" + 'LazyEq h o I1 I2 = (tdeq_ext h o I1 I2). 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 df82586f0..80e174651 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 @@ -125,6 +125,7 @@ table { ] class "cyan" [ { "rt-transition" * } { +(* [ { "uncounted rst-transition" * } { [ "fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )" "fpbq_aaa" * ] [ "fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lfdeq" * ] @@ -142,13 +143,13 @@ table { [ "cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" "cpx_simple" + "cpx_drops" + "cpx_fqus" + "cpx_lsubr" + "cpx_lfxs" * ] } ] +*) [ { "counted context-sensitive rt-transition" * } { [ "cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )" "cpg_simple" + "cpg_drops" + "cpg_lsubr" * ] } ] } ] -*) class "water" [ { "iterated static typing" * } { [ { "iterated extension on referred entries" * } { @@ -241,8 +242,9 @@ table { [ "theq ( ? ⩳[?,?] ? )" "theq_simple" + "theq_tdeq" + "theq_theq" + "theq_simple_vector" * ] } ] - [ { "degree-based equivalence for terms" * } { - [ "tdeq ( ? ≡[?,?] ? ) " "tdeq_ext" + "tdeq_tdeq" * ] + [ { "degree-based equivalence" * } { + [ "tdeq_ext ( ? ≡[?,?] ? )" * ] + [ "tdeq ( ? ≡[?,?] ? )" "tdeq_tdeq" * ] } ] [ { "closures" * } { -- 2.39.2