From 52616a7a6a550efd75ed56e7e246132453506002 Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Sat, 21 Jan 2017 14:34:59 +0000 Subject: [PATCH] - improved fqu allows to prove fqu_cpx_trans and its derivatives - parked frees_fqus_drops that does not hold anymore --- .../basic_2/etc_new/frees/frees_fqus.etc | 111 +++++++++++ .../basic_2/rt_transition/cpx_fqus.ma | 54 +++--- .../basic_2/s_computation/fqup_drops.ma | 8 +- .../lambdadelta/basic_2/s_computation/fqus.ma | 88 ++++++--- .../basic_2/s_computation/fqus_drops.ma | 3 +- .../lambdadelta/basic_2/s_transition/fqu.ma | 181 +++++++++--------- .../lambdadelta/basic_2/static/frees.ma | 18 ++ .../lambdadelta/basic_2/static/frees_fqus.ma | 93 --------- .../lambdadelta/basic_2/web/basic_2_src.tbl | 2 +- .../lambdadelta/ground_2/lib/arith.ma | 4 + 10 files changed, 321 insertions(+), 241 deletions(-) create mode 100644 matita/matita/contribs/lambdadelta/basic_2/etc_new/frees/frees_fqus.etc delete mode 100644 matita/matita/contribs/lambdadelta/basic_2/static/frees_fqus.ma diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_new/frees/frees_fqus.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_new/frees/frees_fqus.etc new file mode 100644 index 000000000..618d858ff --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/etc_new/frees/frees_fqus.etc @@ -0,0 +1,111 @@ +(**************************************************************************) +(* ___ *) +(* ||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_weight.ma". +include "basic_2/s_computation/fqup_weight.ma". +include "basic_2/s_computation/fqus_weight.ma". +include "basic_2/static/frees.ma". + +(* CONTEXT-SENSITIVE FREE VARIABLES *****************************************) + +(* Properties with star-iterated supclosure *********************************) + +(* Note: Restrict fqu_drop on atoms to prove frees_fqus_drops + Counterex: ⦃⋆, ⋆.ⓛ#0, ⓛ#1.#0⦄ ⊐ ⦃⋆, ⋆, ⓛ#0.#0⦄ ⊐ ⦃⋆, ⋆.ⓛ#0, #0⦄ +*) +lemma frees_fqus_drops: ∀G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 → + ∀L2,T2. ⦃G, L1, T1⦄ ⊐* ⦃G, L2, T2⦄ → + ∀I,n. ⬇*[n] L1 ≡ L2.ⓑ{I}T2 → + ∃∃f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & f2 ⊆ ⫱*[⫯n] f1. +#G #L1 #T1 @(fqup_wf_ind_eq … G L1 T1) -G -L1 -T1 +#G0 #L0 #T0 #IH #G #L1 * * +[ #s #HG #HL #HT #f1 #Hf1 #L2 #T2 #H12 #I #n #HL12 destruct + lapply (frees_inv_sort … Hf1) -Hf1 #Hf1 + elim (fqus_inv_sort1 … H12) -H12 * [| elim (nat_split n) ] + [ -IH #H1 #H2 #H3 destruct + lapply (drops_fwd_lw … HL12) -HL12 #HL12 + elim (lt_le_false … HL12) -HL12 // + | -IH #Hn #J #L #V #H12 #H destruct + lapply (drops_fwd_isid … HL12 ?) -HL12 // #H destruct + <(fqus_inv_refl_atom3 … H12) -H12 + /3 width=3 by frees_sort_gen, sle_isid_sn, ex2_intro/ + | * #m #Hn #J #L #V #H12 #H destruct + lapply (drops_inv_drop1 … HL12) -HL12 #HL12 + elim (IH … H12 … HL12) -IH -H12 -HL12 + /3 width=3 by frees_sort_gen, fqu_fqup, fqu_drop, lifts_sort, isid_tl, ex2_intro/ + ] +| #i #HG #HL #HT #f1 #Hf1 #L2 #T2 #H12 #I #n #HL12 destruct + elim (fqus_inv_lref1 … H12) -H12 * [|2,3: elim (nat_split n) ] + [ -IH #H1 #H2 #H3 destruct + lapply (drops_fwd_lw … HL12) -HL12 #HL12 + elim (lt_le_false … HL12) -HL12 // + | -IH #Hn #J #L #V #H12 #H1 #H2 destruct + elim (frees_inv_zero_pair … Hf1) -Hf1 #g1 #Hg1 #H destruct + lapply (drops_fwd_isid … HL12 ?) -HL12 -H12 // #H destruct + /2 width=3 by sle_refl, ex2_intro/ + | * #m #Hn #J #L #V #H12 #H1 #H2 destruct + elim (frees_inv_zero_pair … Hf1) -Hf1 #g1 #Hg1 #H destruct + lapply (drops_inv_drop1 … HL12) -HL12 #HL12 + elim (IH … H12 … HL12) -IH -H12 -HL12 + /2 width=3 by fqu_fqup, fqu_lref_O, ex2_intro/ + | -IH #Hn #J #L #V #j #H12 #H1 #H2 destruct + elim (frees_inv_lref_pair … Hf1) -Hf1 #g1 #Hg1 #H destruct + lapply (drops_fwd_isid … HL12 ?) -HL12 // #H destruct + <(fqus_inv_refl_atom3 … H12) -H12 /2 width=3 by sle_refl, ex2_intro/ + | * #m #Hn #J #L #V #j #H12 #H1 #H2 destruct + elim (frees_inv_lref_pair … Hf1) -Hf1 #g1 #Hg1 #H destruct + lapply (drops_inv_drop1 … HL12) -HL12 #HL12 + elim (IH … H12 … HL12) -IH -H12 -HL12 /2 width=3 by fqu_fqup, ex2_intro/ + ] +| #l #HG #HL #HT #f1 #Hf1 #L2 #T2 #H12 #I #n #HL12 destruct + lapply (frees_inv_gref … Hf1) -Hf1 #Hf1 + elim (fqus_inv_gref1 … H12) -H12 * [| elim (nat_split n) ] + [ -IH #H1 #H2 #H3 destruct + lapply (drops_fwd_lw … HL12) -HL12 #HL12 + elim (lt_le_false … HL12) -HL12 // + | -IH #Hn #J #L #V #H12 #H destruct + lapply (drops_fwd_isid … HL12 ?) -HL12 // #H destruct + <(fqus_inv_refl_atom3 … H12) -H12 + /3 width=3 by frees_gref_gen, sle_isid_sn, ex2_intro/ + | * #m #Hn #J #L #V #H12 #H destruct + lapply (drops_inv_drop1 … HL12) -HL12 #HL12 + elim (IH … H12 … HL12) -IH -H12 -HL12 + /3 width=3 by frees_gref_gen, fqu_fqup, fqu_drop, lifts_sort, isid_tl, ex2_intro/ + ] +| #p #I #V1 #T1 #HG #HL #HT #f1 #Hf1 #L2 #T2 #H12 #I #n #HL12 destruct + elim (frees_inv_bind … Hf1) -Hf1 #f1V #f1T #Hf1V #Hf1T #Hf1 + elim (fqus_inv_bind1 … H12) -H12 + [ -IH -f1V -f1T * #H1 #H2 #H3 destruct + lapply (drops_fwd_lw … HL12) -HL12 #HL12 + elim (lt_le_false … HL12) -HL12 // + | #H12 elim (IH … H12 … HL12) -IH -H12 -HL12 + /4 width=6 by sor_tls, sor_inv_sle_sn_trans, ex2_intro/ + | #H12 elim (IH … H12 I (⫯n)) -IH -H12 [|*: /2 width=3 by drops_drop, drops_refl/ ] -HL12 +