From: Ferruccio Guidi Date: Wed, 18 May 2016 18:44:46 +0000 (+0000) Subject: - ground_2: support for lifts_div4 X-Git-Tag: make_still_working~589 X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=commitdiff_plain;h=384b04944ac31922ee41418b106b8e19a19ba9f0 - ground_2: support for lifts_div4 - basic_2: cpg_drops competed --- diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_new/cpg/cpg_drops.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_new/cpg/cpg_drops.etc new file mode 100644 index 000000000..c0447ffde --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/etc_new/cpg/cpg_drops.etc @@ -0,0 +1,16 @@ +lemma cpg_delift: ∀c,h,I,G,K,V,T1,L,i. ⬇*[i] L ≡ (K.ⓑ{I}V) → + ∃∃T2,T. ⦃G, L⦄ ⊢ T1 ➡[h, 𝟘𝟘] T2 & ⬆*[↑1] T ≡ T2. +#h #c #I #G #K #V #T1 elim T1 -T1 +[ * #i #L #l /2 width=4 by cpg_atom, lift_sort, lift_gref, ex2_2_intro/ + elim (lt_or_eq_or_gt i l) #Hil [1,3: /4 width=4 by cpg_atom, lift_lref_ge_minus, lift_lref_lt, ylt_inj, yle_inj, ex2_2_intro/ ] + destruct + elim (lift_total V 0 (i+1)) #W #HVW + elim (lift_split … HVW i i) /3 width=7 by cpg_delta, ex2_2_intro/ +| * [ #a ] #I #W1 #U1 #IHW1 #IHU1 #L #l #HLK + elim (IHW1 … HLK) -IHW1 #W2 #W #HW12 #HW2 + [ elim (IHU1 (L. ⓑ{I} W1) (l+1)) -IHU1 /3 width=9 by cpg_bind, drop_drop, lift_bind, ex2_2_intro/ + | elim (IHU1 … HLK) -IHU1 -HLK /3 width=8 by cpg_flat, lift_flat, ex2_2_intro/ + ] +] +qed-. +*) diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_new/cpg/cpg_length.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_new/cpg/cpg_length.etc new file mode 100644 index 000000000..142f0fd2c --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/etc_new/cpg/cpg_length.etc @@ -0,0 +1,26 @@ +(**************************************************************************) +(* ___ *) +(* ||M|| *) +(* ||A|| A project by Andrea Asperti *) +(* ||T|| *) +(* ||I|| Developers: *) +(* ||T|| The HELM team. *) +(* ||A|| http://helm.cs.unibo.it *) +(* \ / *) +(* \ / This file is distributed under the terms of the *) +(* v GNU General Public License Version 2 *) +(* *) +(**************************************************************************) + +include "basic_2/relocation/drops.ma". +include "basic_2/rt_transition/cpg.ma". + +(* CONTEXT-SENSITIVE GENERIC PARALLEL RT-TRANSITION FOR TERMS ***************) + +(* Properties with length for local environments ****************************) + +lemma cpg_inv_lref1_ge: ∀h,c,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[h, c] T2 → |L| ≤ i → T2 = #i. +#h #c #G #L #T2 #i #H elim (cpg_inv_lref1 … H) -H // * +#I #K #V1 #V2 #HLK #_ #_ #HL -h -G -V2 lapply (drop_fwd_length_lt2 … HLK) -K -I -V1 +#H elim (lt_refl_false i) /2 width=3 by lt_to_le_to_lt/ +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma index 06a2eb84e..0b3279de9 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma @@ -31,7 +31,7 @@ theorem drops_conf: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≡ L → #g #Hg #H destruct /3 width=3 by drops_inv_drop1/ | #f1 #I #K1 #K #V1 #V #_ #HV1 #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_pxx … Hf) -Hf [1,3: * |*:// ] #g2 #g #Hf #H1 #H2 destruct - [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, lifts_div/ + [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, lifts_div3/ | /4 width=3 by drops_inv_drop1, drops_drop/ ] ] diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma index ceaca58a9..495d5e45f 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma @@ -208,6 +208,8 @@ lemma lifts_inv_flat2: ∀f:rtmap. ∀I,V2,T2,X. ⬆*[f] X ≡ ⓕ{I}V2.T2 → X = ⓕ{I}V1.T1. /2 width=3 by lifts_inv_flat2_aux/ qed-. +(* Advanced inversion lemmas ************************************************) + (* Basic_2A1: includes: lift_inv_pair_xy_x *) lemma lifts_inv_pair_xy_x: ∀f,I,V,T. ⬆*[f] ②{I}V.T ≡ V → ⊥. #f #J #V elim V -V @@ -241,6 +243,10 @@ lemma lifts_inv_pair_xy_y: ∀I,T,V,f. ⬆*[f] ②{I}V.T ≡ T → ⊥. ] qed-. +lemma lifts_inv_lref1_uni: ∀l,Y,i. ⬆*[l] #i ≡ Y → Y = #(l+i). +#l #Y #i1 #H elim (lifts_inv_lref1 … H) -H /4 width=4 by at_mono, eq_f/ +qed-. + (* Basic forward lemmas *****************************************************) (* Basic_2A1: includes: lift_inv_O2 *) @@ -371,6 +377,11 @@ lemma is_lifts_dec: ∀T2,f. Decidable (∃T1. ⬆*[f] T1 ≡ T2). ] qed-. +(* Properties with uniform relocation ***************************************) + +lemma lifts_uni: ∀n1,n2,T,U. ⬆*[𝐔❴n1❵∘𝐔❴n2❵] T ≡ U → ⬆*[n1+n2] T ≡ U. +/3 width=4 by lifts_eq_repl_back, after_inv_total/ qed. + (* Basic_2A1: removed theorems 14: lifts_inv_nil lifts_inv_cons lift_inv_Y1 lift_inv_Y2 lift_inv_lref_Y1 lift_inv_lref_Y2 lift_lref_Y lift_Y1 diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts.ma index 79c200087..8477714f3 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts.ma @@ -20,17 +20,48 @@ include "basic_2/relocation/lifts.ma". (* Basic_1: includes: lift_gen_lift *) (* Basic_2A1: includes: lift_div_le lift_div_be *) -theorem lifts_div: ∀f2,T,T2. ⬆*[f2] T2 ≡ T → ∀T1,f. ⬆*[f] T1 ≡ T → - ∀f1. f2 ⊚ f1 ≡ f → ⬆*[f1] T1 ≡ T2. +theorem lift_div4: ∀f2,Tf,T. ⬆*[f2] Tf ≡ T → ∀g2,Tg. ⬆*[g2] Tg ≡ T → + ∀f1,g1. H_at_div f2 g2 f1 g1 → + ∃∃T0. ⬆*[f1] T0 ≡ Tf & ⬆*[g1] T0 ≡ Tg. +#f2 #Tf #T #H elim H -f2 -Tf -T +[ #f2 #s #g2 #Tg #H #f1 #g1 #_ + lapply (lifts_inv_sort2 … H) -H #H destruct + /2 width=3 by ex2_intro/ +| #f2 #jf #j #Hf2 #g2 #Tg #H #f1 #g1 #H0 + elim (lifts_inv_lref2 … H) -H #jg #Hg2 #H destruct + elim (H0 … Hf2 Hg2) -H0 -j /3 width=3 by lifts_lref, ex2_intro/ +| #f2 #l #g2 #Tg #H #f1 #g1 #_ + lapply (lifts_inv_gref2 … H) -H #H destruct + /2 width=3 by ex2_intro/ +| #f2 #p #I #Vf #V #Tf #T #_ #_ #IHV #IHT #g2 #X #H #f1 #g1 #H0 + elim (lifts_inv_bind2 … H) -H #Vg #Tg #HVg #HTg #H destruct + elim (IHV … HVg … H0) -IHV -HVg + elim (IHT … HTg) -IHT -HTg [ |*: /2 width=8 by at_div_pp/ ] + /3 width=5 by lifts_bind, ex2_intro/ +| #f2 #I #Vf #V #Tf #T #_ #_ #IHV #IHT #g2 #X #H #f1 #g1 #H0 + elim (lifts_inv_flat2 … H) -H #Vg #Tg #HVg #HTg #H destruct + elim (IHV … HVg … H0) -IHV -HVg + elim (IHT … HTg … H0) -IHT -HTg -H0 + /3 width=5 by lifts_flat, ex2_intro/ +] +qed-. + +lemma lifts_div4_one: ∀f,Tf,T. ⬆*[↑f] Tf ≡ T → + ∀T1. ⬆*[1] T1 ≡ T → + ∃∃T0. ⬆*[1] T0 ≡ Tf & ⬆*[f] T0 ≡ T1. +/4 width=6 by lift_div4, at_div_id_dx, at_div_pn/ qed-. + +theorem lifts_div3: ∀f2,T,T2. ⬆*[f2] T2 ≡ T → ∀f,T1. ⬆*[f] T1 ≡ T → + ∀f1. f2 ⊚ f1 ≡ f → ⬆*[f1] T1 ≡ T2. #f2 #T #T2 #H elim H -f2 -T -T2 -[ #f2 #s #T1 #f #H >(lifts_inv_sort2 … H) -T1 // -| #f2 #i2 #i #Hi2 #T1 #f #H #f1 #Ht21 elim (lifts_inv_lref2 … H) -H +[ #f2 #s #f #T1 #H >(lifts_inv_sort2 … H) -T1 // +| #f2 #i2 #i #Hi2 #f #T1 #H #f1 #Ht21 elim (lifts_inv_lref2 … H) -H #i1 #Hi1 #H destruct /3 width=6 by lifts_lref, after_fwd_at1/ -| #f2 #l #T1 #f #H >(lifts_inv_gref2 … H) -T1 // -| #f2 #p #I #W2 #W #U2 #U #_ #_ #IHW #IHU #T1 #f #H +| #f2 #l #f #T1 #H >(lifts_inv_gref2 … H) -T1 // +| #f2 #p #I #W2 #W #U2 #U #_ #_ #IHW #IHU #f #T1 #H elim (lifts_inv_bind2 … H) -H #W1 #U1 #HW1 #HU1 #H destruct /4 width=3 by lifts_bind, after_O2/ -| #f2 #I #W2 #W #U2 #U #_ #_ #IHW #IHU #T1 #f #H +| #f2 #I #W2 #W #U2 #U #_ #_ #IHW #IHU #f #T1 #H elim (lifts_inv_flat2 … H) -H #W1 #U1 #HW1 #HU1 #H destruct /3 width=3 by lifts_flat/ ] @@ -39,34 +70,34 @@ qed-. (* Basic_1: was: lift1_lift1 (left to right) *) (* Basic_1: includes: lift_free (left to right) lift_d lift1_xhg (right to left) lift1_free (right to left) *) (* Basic_2A1: includes: lift_trans_be lift_trans_le lift_trans_ge lifts_lift_trans_le lifts_lift_trans *) -theorem lifts_trans: ∀f1,T1,T. ⬆*[f1] T1 ≡ T → ∀T2,f2. ⬆*[f2] T ≡ T2 → +theorem lifts_trans: ∀f1,T1,T. ⬆*[f1] T1 ≡ T → ∀f2,T2. ⬆*[f2] T ≡ T2 → ∀f. f2 ⊚ f1 ≡ f → ⬆*[f] T1 ≡ T2. #f1 #T1 #T #H elim H -f1 -T1 -T -[ #f1 #s #T2 #f2 #H >(lifts_inv_sort1 … H) -T2 // -| #f1 #i1 #i #Hi1 #T2 #f2 #H #f #Ht21 elim (lifts_inv_lref1 … H) -H +[ #f1 #s #f2 #T2 #H >(lifts_inv_sort1 … H) -T2 // +| #f1 #i1 #i #Hi1 #f2 #T2 #H #f #Ht21 elim (lifts_inv_lref1 … H) -H #i2 #Hi2 #H destruct /3 width=6 by lifts_lref, after_fwd_at/ -| #f1 #l #T2 #f2 #H >(lifts_inv_gref1 … H) -T2 // -| #f1 #p #I #W1 #W #U1 #U #_ #_ #IHW #IHU #T2 #f2 #H +| #f1 #l #f2 #T2 #H >(lifts_inv_gref1 … H) -T2 // +| #f1 #p #I #W1 #W #U1 #U #_ #_ #IHW #IHU #f2 #T2 #H elim (lifts_inv_bind1 … H) -H #W2 #U2 #HW2 #HU2 #H destruct /4 width=3 by lifts_bind, after_O2/ -| #f1 #I #W1 #W #U1 #U #_ #_ #IHW #IHU #T2 #f2 #H +| #f1 #I #W1 #W #U1 #U #_ #_ #IHW #IHU #f2 #T2 #H elim (lifts_inv_flat1 … H) -H #W2 #U2 #HW2 #HU2 #H destruct /3 width=3 by lifts_flat/ ] qed-. (* Basic_2A1: includes: lift_conf_O1 lift_conf_be *) -theorem lifts_conf: ∀f1,T,T1. ⬆*[f1] T ≡ T1 → ∀T2,f. ⬆*[f] T ≡ T2 → +theorem lifts_conf: ∀f1,T,T1. ⬆*[f1] T ≡ T1 → ∀f,T2. ⬆*[f] T ≡ T2 → ∀f2. f2 ⊚ f1 ≡ f → ⬆*[f2] T1 ≡ T2. #f1 #T #T1 #H elim H -f1 -T -T1 -[ #f1 #s #T2 #f #H >(lifts_inv_sort1 … H) -T2 // -| #f1 #i #i1 #Hi1 #T2 #f #H #f2 #Ht21 elim (lifts_inv_lref1 … H) -H +[ #f1 #s #f #T2 #H >(lifts_inv_sort1 … H) -T2 // +| #f1 #i #i1 #Hi1 #f #T2 #H #f2 #Ht21 elim (lifts_inv_lref1 … H) -H #i2 #Hi2 #H destruct /3 width=6 by lifts_lref, after_fwd_at2/ -| #f1 #l #T2 #f #H >(lifts_inv_gref1 … H) -T2 // -| #f1 #p #I #W #W1 #U #U1 #_ #_ #IHW #IHU #T2 #f #H +| #f1 #l #f #T2 #H >(lifts_inv_gref1 … H) -T2 // +| #f1 #p #I #W #W1 #U #U1 #_ #_ #IHW #IHU #f #T2 #H elim (lifts_inv_bind1 … H) -H #W2 #U2 #HW2 #HU2 #H destruct /4 width=3 by lifts_bind, after_O2/ -| #f1 #I #W #W1 #U #U1 #_ #_ #IHW #IHU #T2 #f #H +| #f1 #I #W #W1 #U #U1 #_ #_ #IHW #IHU #f #T2 #H elim (lifts_inv_flat1 … H) -H #W2 #U2 #HW2 #HU2 #H destruct /3 width=3 by lifts_flat/ ] @@ -77,7 +108,7 @@ qed-. (* Basic_2A1: includes: lift_inj *) lemma lifts_inj: ∀f,T1,U. ⬆*[f] T1 ≡ U → ∀T2. ⬆*[f] T2 ≡ U → T1 = T2. #f #T1 #U #H1 #T2 #H2 lapply (isid_after_dx 𝐈𝐝 … f) -/3 width=6 by lifts_div, lifts_fwd_isid/ +/3 width=6 by lifts_div3, lifts_fwd_isid/ qed-. (* Basic_2A1: includes: lift_mono *) 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 12c45c9fe..22c671d90 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma @@ -30,7 +30,7 @@ inductive cpg (h): rtc → relation4 genv lenv term term ≝ ⬆*[1] V2 ≡ W2 → cpg h (↓c) G (L.ⓓV1) (#0) W2 | cpg_ell : ∀c,G,L,V1,V2,W2. cpg h c G L V1 V2 → ⬆*[1] V2 ≡ W2 → cpg h ((↓c)+𝟘𝟙) G (L.ⓛV1) (#0) W2 -| cpt_lref : ∀c,I,G,L,V,T,U,i. cpg h c G L (#i) T → +| cpg_lref : ∀c,I,G,L,V,T,U,i. cpg h c G L (#i) T → ⬆*[1] T ≡ U → cpg h c G (L.ⓑ{I}V) (#⫯i) U | cpg_bind : ∀cV,cT,p,I,G,L,V1,V2,T1,T2. cpg h cV G L V1 V2 → cpg h cT G (L.ⓑ{I}V1) T1 T2 → @@ -70,8 +70,8 @@ qed. (* Basic inversion lemmas ***************************************************) fact cpg_inv_atom1_aux: ∀c,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[c, h] T2 → ∀J. T1 = ⓪{J} → - ∨∨ T2 = ⓪{J} - | ∃∃s. J = Sort s & T2 = ⋆(next h s) + ∨∨ T2 = ⓪{J} ∧ c = 𝟘𝟘 + | ∃∃s. J = Sort s & T2 = ⋆(next h s) & c = 𝟘𝟙 | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 & L = K.ⓓV1 & J = LRef 0 & c = ↓cV | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 & @@ -79,8 +79,8 @@ fact cpg_inv_atom1_aux: ∀c,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[c, h] T2 → ∀ | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ➡[c, h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V & J = LRef (⫯i). #c #h #G #L #T1 #T2 * -c -G -L -T1 -T2 -[ #I #G #L #J #H destruct /2 width=1 by or5_intro0/ -| #G #L #s #J #H destruct /3 width=3 by or5_intro1, ex2_intro/ +[ #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/ @@ -95,8 +95,8 @@ fact cpg_inv_atom1_aux: ∀c,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[c, h] T2 → ∀ qed-. lemma cpg_inv_atom1: ∀c,h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[c, h] T2 → - ∨∨ T2 = ⓪{J} - | ∃∃s. J = Sort s & T2 = ⋆(next h s) + ∨∨ T2 = ⓪{J} ∧ c = 𝟘𝟘 + | ∃∃s. J = Sort s & T2 = ⋆(next h s) & c = 𝟘𝟙 | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 & L = K.ⓓV1 & J = LRef 0 & c = ↓cV | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 & @@ -106,23 +106,23 @@ lemma cpg_inv_atom1: ∀c,h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[c, h] T2 → /2 width=3 by cpg_inv_atom1_aux/ qed-. lemma cpg_inv_sort1: ∀c,h,G,L,T2,s. ⦃G, L⦄ ⊢ ⋆s ➡[c, h] T2 → - T2 = ⋆s ∨ T2 = ⋆(next h s). + (T2 = ⋆s ∧ c = 𝟘𝟘) ∨ (T2 = ⋆(next h s) ∧ c = 𝟘𝟙). #c #h #G #L #T2 #s #H -elim (cpg_inv_atom1 … H) -H /2 width=1 by or_introl/ * -[ #s0 #H destruct /2 width=1 by or_intror/ +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 ] qed-. lemma cpg_inv_zero1: ∀c,h,G,L,T2. ⦃G, L⦄ ⊢ #0 ➡[c, h] T2 → - ∨∨ T2 = #0 + ∨∨ (T2 = #0 ∧ c = 𝟘𝟘) | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 & L = K.ⓓV1 & c = ↓cV | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 & L = K.ⓛV1 & c = (↓cV)+𝟘𝟙. #c #h #G #L #T2 #H -elim (cpg_inv_atom1 … H) -H /2 width=1 by or3_intro0/ * +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 @@ -130,19 +130,19 @@ elim (cpg_inv_atom1 … H) -H /2 width=1 by or3_intro0/ * qed-. lemma cpg_inv_lref1: ∀c,h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ➡[c, h] T2 → - (T2 = #⫯i) ∨ + (T2 = #(⫯i) ∧ c = 𝟘𝟘) ∨ ∃∃I,K,V,T. ⦃G, K⦄ ⊢ #i ➡[c, h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V. #c #h #G #L #T2 #i #H -elim (cpg_inv_atom1 … H) -H /2 width=1 by or_introl/ * +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/ ] qed-. -lemma cpg_inv_gref1: ∀c,h,G,L,T2,l. ⦃G, L⦄ ⊢ §l ➡[c, h] T2 → T2 = §l. +lemma cpg_inv_gref1: ∀c,h,G,L,T2,l. ⦃G, L⦄ ⊢ §l ➡[c, h] T2 → T2 = §l ∧ c = 𝟘𝟘. #c #h #G #L #T2 #l #H -elim (cpg_inv_atom1 … H) -H // * +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 @@ -190,9 +190,9 @@ lemma cpg_inv_abbr1: ∀c,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ➡[c, h] /3 width=8 by ex4_4_intro, ex4_2_intro, or_introl, or_intror/ qed-. -lemma cpg_inv_abst1: ∀c,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ➡[c, h] U2 → +lemma cpg_inv_abst1: ∀c,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ➡[c, h] U2 → ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ➡[cV, h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ➡[cT, h] T2 & - U2 = ⓛ{p} V2. T2 & c = (↓cV)+cT. + U2 = ⓛ{p}V2.T2 & c = (↓cV)+cT. #c #h #p #G #L #V1 #T1 #U2 #H elim (cpg_inv_bind1 … H) -H * [ /3 width=8 by ex4_4_intro/ | #c #T #_ #_ #_ #H destruct 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 6a235c4d9..4ccf66fdf 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 @@ -12,36 +12,191 @@ (* *) (**************************************************************************) -include "basic_2/relocation/drops.ma". +include "basic_2/relocation/drops_drops.ma". +include "basic_2/s_computation/fqup_weight.ma". +include "basic_2/s_computation/fqup_drops.ma". include "basic_2/rt_transition/cpg.ma". (* CONTEXT-SENSITIVE GENERIC PARALLEL RT-TRANSITION FOR TERMS ***************) +(* Advanced properties ******************************************************) + +lemma cpg_delta_drops: ∀c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V ➡[c, h] V2 → + ⬆*[⫯i] V2 ≡ T2 → ⦃G, L⦄ ⊢ #i ➡[↓c, h] T2. +#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 (lifts_split_trans … HVT2 (𝐔❴⫯i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/ +] +qed. + +lemma cpg_ell_drops: ∀c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≡ K.ⓛV → ⦃G, K⦄ ⊢ V ➡[c, h] V2 → + ⬆*[⫯i] V2 ≡ T2 → ⦃G, L⦄ ⊢ #i ➡[(↓c)+𝟘𝟙, h] T2. +#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 (lifts_split_trans … HVT2 (𝐔❴⫯i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/ +] +qed. + +(* Advanced inversion lemmas ************************************************) + +lemma cpg_inv_lref1_drops: ∀c,h,G,i,L,T2. ⦃G, L⦄ ⊢ #i ➡[c, h] T2 → + ∨∨ T2 = #i ∧ c = 𝟘𝟘 + | ∃∃cV,K,V,V2. ⬇*[i] L ≡ K.ⓓV & ⦃G, K⦄ ⊢ V ➡[cV, h] V2 & + ⬆*[⫯i] V2 ≡ T2 & c = ↓cV + | ∃∃cV,K,V,V2. ⬇*[i] L ≡ K.ⓛV & ⦃G, K⦄ ⊢ V ➡[cV, h] V2 & + ⬆*[⫯i] V2 ≡ T2 & c = (↓cV) + 𝟘𝟙. +#c #h #G #i elim i -i +[ #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 + [ * #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 + /4 width=8 by drops_drop, ex4_4_intro, or3_intro2, or3_intro1/ +] +qed-. + (* Properties with generic slicing for local environments *******************) -lemma cpg_delift: ∀c,h,I,G,K,V,T1,L,i. ⬇*[i] L ≡ (K.ⓑ{I}V) → - ∃∃T2,T. ⦃G, L⦄ ⊢ T1 ➡[h, 𝟘𝟘] T2 & ⬆*[↑1] T ≡ T2. -#h #c #I #G #K #V #T1 elim T1 -T1 -[ * #i #L #l /2 width=4 by cpg_atom, lift_sort, lift_gref, ex2_2_intro/ - elim (lt_or_eq_or_gt i l) #Hil [1,3: /4 width=4 by cpg_atom, lift_lref_ge_minus, lift_lref_lt, ylt_inj, yle_inj, ex2_2_intro/ ] - destruct - elim (lift_total V 0 (i+1)) #W #HVW - elim (lift_split … HVW i i) /3 width=7 by cpg_delta, ex2_2_intro/ -| * [ #a ] #I #W1 #U1 #IHW1 #IHU1 #L #l #HLK - elim (IHW1 … HLK) -IHW1 #W2 #W #HW12 #HW2 - [ elim (IHU1 (L. ⓑ{I} W1) (l+1)) -IHU1 /3 width=9 by cpg_bind, drop_drop, lift_bind, ex2_2_intro/ - | elim (IHU1 … HLK) -IHU1 -HLK /3 width=8 by cpg_flat, lift_flat, ex2_2_intro/ +lemma cpg_lifts: ∀c,h,G. d_liftable2 (cpg h c G). +#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 * * +[ #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 + /2 width=3 by cpg_atom, cpg_ess, lifts_sort, ex2_intro/ +| #i1 #HG #HK #HT #c #T2 #H2 #b #f #L #HLK #X1 #H1 destruct + elim (cpg_inv_lref1_drops … H2) -H2 * + [ #H1 #H2 destruct /2 width=3 by ex2_intro/ ] + #cV #K0 #V #V2 #HK0 #HV2 #HVT2 #H destruct + elim (lifts_inv_lref1 … H1) -H1 #i2 #Hf #H destruct + 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_inv_tls_at … Hf … HY) -HY #HY + elim (drops_inv_skip2 … HY) -HY #L0 #W #HLK0 #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 + lapply (lifts_conf … HVT2 … HVU2 f ?) -V2 [1,3: /2 width=3 by after_uni_succ_sn/ ] + /4 width=8 by cpg_ell_drops, cpg_delta_drops, drops_inv_gen, ex2_intro/ +| #l #HG #HK #HT #c #X2 #H2 #b #f #L #HLK #X1 #H1 destruct -IH + lapply (lifts_inv_gref1 … H1) -H1 #H destruct + elim (cpg_inv_gref1 … H2) -H2 #H1 #H2 destruct + /2 width=3 by cpg_atom, lifts_gref, ex2_intro/ +| #p #I #V1 #T1 #HG #HK #HT #c #X2 #H2 #b #f #L #HLK #X1 #H1 destruct + elim (lifts_inv_bind1 … H1) -H1 #W1 #U1 #HVW1 #HTU1 #H destruct + 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/ ] + /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 + 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/ + ] +| #I #V1 #T1 #HG #HK #HT #c #X2 #H2 #b #f #L #HLK #X1 #H1 destruct + elim (lifts_inv_flat1 … H1) -H1 #W1 #U1 #HVW1 #HTU1 #H destruct + elim (cpg_inv_flat1 … H2) -H2 * + [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct + elim (IH … HV12 … HLK … HVW1) -HV12 -HVW1 // + elim (IH … HT12 … HLK … HTU1) -IH -HT12 -HLK -HTU1 // + /3 width=5 by cpg_flat, lifts_flat, ex2_intro/ + | #cT #HT12 #H1 #H2 destruct + elim (IH … HT12 … HLK … HTU1) -IH -HT12 -HLK -HTU1 // + /3 width=3 by cpg_eps, ex2_intro/ + | #cV #HV12 #H1 #H2 destruct + elim (IH … HV12 … HLK … HVW1) -IH -HV12 -HLK -HVW1 // + /3 width=3 by cpg_ee, ex2_intro/ + | #cV #cY #cT #a #V2 #Y1 #Y2 #T0 #T2 #HV12 #HY12 #HT12 #H1 #H2 #H3 #H4 destruct + 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/ ] + /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 #H4 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 (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/ + /4 width=9 by cpg_theta, lifts_bind, lifts_flat, ex2_intro/ ] ] qed-. -lemma cpg_inv_lref1: ∀h,c,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[h, c] T2 → - T2 = #i ∨ - ∃∃I,K,V,V2. ⬇[i] L ≡ K. ⓑ{I}V & ⦃G, K⦄ ⊢ V ➡[h, c] V2 & - ⬆[O, i+1] V2 ≡ T2. -#h #c #G #L #T2 #i #H -elim (cpg_inv_atom1 … H) -H /2 width=1 by or_introl/ * -[ #s #d #_ #_ #H destruct -| #I #K #V #V2 #j #HLK #HV2 #HVT2 #H destruct /3 width=7 by ex3_4_intro, or_intror/ +(* Inversion lemmas with generic slicing for local environments *************) + +lemma cpg_inv_lift1: ∀c,h,G. d_deliftable2_sn (cpg h c G). +#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 * * +[ #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 + /2 width=3 by cpg_atom, cpg_ess, lifts_sort, ex2_intro/ +| #i2 #HG #HL #HU #c #U2 #H2 #b #f #K #HLK #X1 #H1 destruct + elim (cpg_inv_lref1_drops … H2) -H2 * + [ #H1 #H2 destruct /2 width=3 by ex2_intro/ ] + #cW #L0 #W #W2 #HL0 #HW2 #HWU2 #H destruct + elim (lifts_inv_lref2 … H1) -H1 #i1 #Hf #H destruct + 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_inv_tls_at … Hf … HLY0) -HLY0 #HLY0 + elim (drops_inv_skip1 … HLY0) -HLY0 #K0 #V #HLK0 #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/ ] + /4 width=8 by cpg_ell_drops, cpg_delta_drops, drops_inv_F, ex2_intro/ +| #l #HG #HL #HU #c #X2 #H2 #b #f #K #HLK #X1 #H1 destruct -IH + lapply (lifts_inv_gref2 … H1) -H1 #H destruct + elim (cpg_inv_gref1 … H2) -H2 #H1 #H2 destruct + /2 width=3 by cpg_atom, lifts_gref, ex2_intro/ +| #p #I #W1 #U1 #HG #HL #HU #c #X2 #H2 #b #f #K #HLK #X1 #H1 destruct + elim (lifts_inv_bind2 … H1) -H1 #V1 #T1 #HVW1 #HTU1 #H destruct + 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/ ] + /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 (lifts_div4_one … HTU2 … HXU2) -U2 /3 width=5 by cpg_zeta, ex2_intro/ + ] +| #I #W1 #U1 #HG #HL #HU #c #X2 #H2 #b #f #K #HLK #X1 #H1 destruct + elim (lifts_inv_flat2 … H1) -H1 #V1 #T1 #HVW1 #HTU1 #H destruct + elim (cpg_inv_flat1 … H2) -H2 * + [ #cW #cU #W2 #U2 #HW12 #HU12 #H1 #H2 destruct + elim (IH … HW12 … HLK … HVW1) -HW12 -HVW1 // + elim (IH … HU12 … HLK … HTU1) -IH -HU12 -HLK -HTU1 // + /3 width=5 by cpg_flat, lifts_flat, ex2_intro/ + | #cU #HU12 #H1 #H2 destruct + elim (IH … HU12 … HLK … HTU1) -IH -HU12 -HLK -HTU1 // + /3 width=3 by cpg_eps, ex2_intro/ + | #cW #HW12 #H1 #H2 destruct + elim (IH … HW12 … HLK … HVW1) -IH -HW12 -HLK -HVW1 // + /3 width=3 by cpg_ee, ex2_intro/ + | #cW #cZ #cU #a #W2 #Z1 #Z2 #U0 #U2 #HW12 #HZ12 #HU12 #H1 #H2 #H3 #H4 destruct + 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/ ] + /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 #H4 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/ ] + 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/ + ] ] qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_length.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_length.ma deleted file mode 100644 index 142f0fd2c..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_length.ma +++ /dev/null @@ -1,26 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -include "basic_2/relocation/drops.ma". -include "basic_2/rt_transition/cpg.ma". - -(* CONTEXT-SENSITIVE GENERIC PARALLEL RT-TRANSITION FOR TERMS ***************) - -(* Properties with length for local environments ****************************) - -lemma cpg_inv_lref1_ge: ∀h,c,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[h, c] T2 → |L| ≤ i → T2 = #i. -#h #c #G #L #T2 #i #H elim (cpg_inv_lref1 … H) -H // * -#I #K #V1 #V2 #HLK #_ #_ #HL -h -G -V2 lapply (drop_fwd_length_lt2 … HLK) -K -I -V1 -#H elim (lt_refl_false i) /2 width=3 by lt_to_le_to_lt/ -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 131d28b9c..f5b94d905 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 @@ -19,8 +19,8 @@ include "basic_2/rt_transition/cpg.ma". (* Properties with restricted refinement for local environments *************) -lemma lsubr_cpg_trans: ∀h,c,G. lsub_trans … (cpg h c G) lsubr. -#h #c #G #L1 #T1 #T2 #H elim H -c -G -L1 -T1 -T2 +lemma lsubr_cpg_trans: ∀c,h,G. lsub_trans … (cpg h c G) lsubr. +#c #h #G #L1 #T1 #T2 #H elim H -c -G -L1 -T1 -T2 [ // | /2 width=2 by cpg_st/ | #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_simple.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_simple.ma index 1c9f06d47..53448a7bb 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_simple.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_simple.ma @@ -12,23 +12,22 @@ (* *) (**************************************************************************) -include "basic_2/relocation/drops.ma". +include "basic_2/grammar/term_simple.ma". include "basic_2/rt_transition/cpg.ma". (* CONTEXT-SENSITIVE GENERIC PARALLEL RT-TRANSITION FOR TERMS ***************) -(* Properties with generic slicing for local environments *******************) +(* Properties with simple terms *********************************************) (* Note: the main property of simple terms *) -lemma cpg_inv_appl1_simple: ∀h,c,G,L,V1,T1,U. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡[h, c] U → 𝐒⦃T1⦄ → - ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h, c] V2 & ⦃G, L⦄ ⊢ T1 ➡[h, c] T2 & - U = ⓐV2.T2. -#h #c #G #L #V1 #T1 #U #H #HT1 -elim (cpg_inv_appl1 … H) -H * -[ /2 width=5 by ex3_2_intro/ -| #a #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #H #_ destruct +lemma cpg_inv_appl1_simple: ∀c,h,G,L,V1,T1,U. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡[c, h] U → 𝐒⦃T1⦄ → + ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ➡[cV, h] V2 & ⦃G, L⦄ ⊢ T1 ➡[cT, h] T2 & + U = ⓐV2.T2 & c = (↓cV)+cT. +#c #h #G #L #V1 #T1 #U #H #HT1 elim (cpg_inv_appl1 … H) -H * +[ /2 width=8 by ex4_4_intro/ +| #cV #cW #cT #p #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #H destruct elim (simple_inv_bind … HT1) -| #a #V #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #_ #H #_ destruct +| #cV #cW #cT #p #V #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #_ #H destruct elim (simple_inv_bind … HT1) ] qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_drops.ma index e388af445..4255a20c4 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_drops.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_drops.ma @@ -22,7 +22,7 @@ include "basic_2/static/aaa.ma". (* Advanced properties ******************************************************) (* Basic_2A1: was: aaa_lref *) -lemma aaa_lref_gen: ∀I,G,K,V,B,i,L. ⬇*[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ⁝ B → ⦃G, L⦄ ⊢ #i ⁝ B. +lemma aaa_lref_drops: ∀I,G,K,V,B,i,L. ⬇*[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ⁝ B → ⦃G, L⦄ ⊢ #i ⁝ B. #I #G #K #V #B #i elim i -i [ #L #H lapply (drops_fwd_isid … H ?) -H // #H destruct /2 width=1 by aaa_zero/ @@ -34,8 +34,8 @@ qed. (* Advanced inversion lemmas ************************************************) (* Basic_2A1: was: aaa_inv_lref *) -lemma aaa_inv_lref_gen: ∀G,A,i,L. ⦃G, L⦄ ⊢ #i ⁝ A → - ∃∃I,K,V. ⬇*[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ⁝ A. +lemma aaa_inv_lref_drops: ∀G,A,i,L. ⦃G, L⦄ ⊢ #i ⁝ A → + ∃∃I,K,V. ⬇*[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ⁝ A. #G #A #i elim i -i [ #L #H elim (aaa_inv_zero … H) -H /3 width=5 by drops_refl, ex2_3_intro/ | #i #IH #L #H elim (aaa_inv_lref … H) -H @@ -53,13 +53,13 @@ lemma aaa_lifts: ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀b,f,L2. ⬇*[b, f lapply (aaa_inv_sort … H) -H #H destruct >(lifts_inv_sort1 … HX) -HX // | #i1 #HG #HL #HT #A #H #b #f #L2 #HL21 #X #HX - elim (aaa_inv_lref_gen … H) -H #J #K1 #V1 #HLK1 #HA + elim (aaa_inv_lref_drops … H) -H #J #K1 #V1 #HLK1 #HA elim (lifts_inv_lref1 … HX) -HX #i2 #Hf #H destruct lapply (drops_trans … HL21 … HLK1 ??) -HL21 [1,2: // ] #H elim (drops_split_trans … H) -H [ |*: /2 width=6 by after_uni_dx/ ] #Y #HLK2 #HY lapply (drops_inv_tls_at … Hf … HY) -HY #HY -Hf elim (drops_inv_skip2 … HY) -HY #K2 #V2 #HK21 #HV12 #H destruct - /4 width=12 by aaa_lref_gen, fqup_lref, drops_inv_gen/ + /4 width=12 by aaa_lref_drops, fqup_lref, drops_inv_gen/ | #l #HG #HL #HT #A #H #b #f #L2 #HL21 #X #HX -b -f -IH elim (aaa_inv_gref … H) | #p * #V1 #T1 #HG #HL #HT #A #H #b #f #L2 #HL21 #X #HX @@ -91,13 +91,13 @@ lemma aaa_inv_lifts: ∀G,L2,T2,A. ⦃G, L2⦄ ⊢ T2 ⁝ A → ∀b,f,L1. ⬇*[ lapply (aaa_inv_sort … H) -H #H destruct >(lifts_inv_sort2 … HX) -HX // | #i2 #HG #HL #HT #A #H #b #f #L1 #HL21 #X #HX - elim (aaa_inv_lref_gen … H) -H #J #K2 #V2 #HLK2 #HA + elim (aaa_inv_lref_drops … H) -H #J #K2 #V2 #HLK2 #HA elim (lifts_inv_lref2 … HX) -HX #i1 #Hf #H destruct lapply (drops_split_div … HL21 (𝐔❴i1❵) ???) -HL21 [4: * |*: // ] #Y #HLK1 #HY lapply (drops_conf … HLK2 … HY ??) -HY [1,2: /2 width=6 by after_uni_dx/ ] #HY lapply (drops_inv_tls_at … Hf … HY) -HY #HY -Hf elim (drops_inv_skip1 … HY) -HY #K1 #V1 #HK21 #HV12 #H destruct - /4 width=12 by aaa_lref_gen, fqup_lref, drops_inv_F/ + /4 width=12 by aaa_lref_drops, fqup_lref, drops_inv_F/ | #l #HG #HL #HT #A #H #b #f #L1 #HL21 #X #HX -IH -b -f elim (aaa_inv_gref … H) | #p * #V2 #T2 #HG #HL #HT #A #H #b #f #L1 #HL21 #X #HX diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_after.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_after.ma index f8b71a6a5..25bb3c60b 100644 --- a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_after.ma +++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_after.ma @@ -129,6 +129,9 @@ lemma after_inv_const: ∀f1,f2,f,n2,n. n@f1 ⊚ n2@f2 ≡ n@f → f1 ⊚ f2 ≡ ] qed-. +lemma after_inv_total: ∀f1,f2,f. f1 ⊚ f2 ≡ f → f1 ∘ f2 ≗ f. +/2 width=4 by after_mono/ qed-. + (* Specific forward lemmas **************************************************) lemma after_fwd_hd: ∀f1,f2,f,n2,n. f1 ⊚ n2@f2 ≡ n@f → f1@❴n2❵ = n. diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_after.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_after.ma index 15969a23c..a00a10d16 100644 --- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_after.ma +++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_after.ma @@ -436,6 +436,50 @@ lemma after_uni_sn: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 → ] qed-. +lemma after_uni_succ_dx: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 → + ∀f. f2 ⊚ 𝐔❴⫯i1❵ ≡ f → 𝐔❴⫯i2❵ ⊚ ⫱*[⫯i2] f2 ≡ f. +#i2 elim i2 -i2 +[ #i1 #f2 #Hf2 #f #Hf + elim (at_inv_xxp … Hf2) -Hf2 // #g2 #H1 #H2 destruct + elim (after_inv_pnx … Hf) -Hf [ |*: // ] #g #Hg #H + lapply (after_isid_inv_dx … Hg ?) -Hg + /4 width=5 by isid_after_sn, after_eq_repl_back_0, after_next/ +| #i2 #IH #i1 #f2 #Hf2 #f #Hf + elim (at_inv_xxn … Hf2) -Hf2 [1,3: * |*: // ] + [ #g2 #j1 #Hg2 #H1 #H2 destruct + elim (after_inv_pnx … Hf) -Hf [ |*: // ] #g #Hg #H destruct + /3 width=5 by after_next/ + | #g2 #Hg2 #H2 destruct + elim (after_inv_nxx … Hf) -Hf [2,3: // ] #g #Hg #H destruct + /3 width=5 by after_next/ + ] +] +qed. + +lemma after_uni_succ_sn: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 → + ∀f. 𝐔❴⫯i2❵ ⊚ ⫱*[⫯i2] f2 ≡ f → f2 ⊚ 𝐔❴⫯i1❵ ≡ f. +#i2 elim i2 -i2 +[ #i1 #f2 #Hf2 #f #Hf + elim (at_inv_xxp … Hf2) -Hf2 // #g2 #H1 #H2 destruct + elim (after_inv_nxx … Hf) -Hf [ |*: // ] #g #Hg #H destruct + lapply (after_isid_inv_sn … Hg ?) -Hg + /4 width=7 by isid_after_dx, after_eq_repl_back_0, after_push/ +| #i2 #IH #i1 #f2 #Hf2 #f #Hf + elim (after_inv_nxx … Hf) -Hf [2,3: // ] #g #Hg #H destruct + elim (at_inv_xxn … Hf2) -Hf2 [1,3: * |*: // ] + [ #g2 #j1 #Hg2 #H1 #H2 destruct