+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/s_computation/fqus_fqup.ma".
-include "basic_2/static/rdeq_drops.ma".
-include "basic_2/static/rdeq_fqup.ma".
-include "basic_2/static/rdeq_rdeq.ma".
-
-(* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
-
-(* Properties with extended structural successor for closures ***************)
-
-lemma fqu_tdeq_conf: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, T1⦄ →
- ∀U2. U1 ≛[h, o] U2 →
- ∃∃L,T2. ⦃G1, L1, U2⦄ ⊐[b] ⦃G2, L, T2⦄ & L2 ≛[h, o, T1] L & T1 ≛[h, o] T2.
-#h #o #b #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -G1 -G2 -L1 -L2 -U1 -T1
-[ #I #G #L #W #X #H >(tdeq_inv_lref1 … H) -X
- /2 width=5 by fqu_lref_O, ex3_2_intro/
-| #I #G #L #W1 #U1 #X #H
- elim (tdeq_inv_pair1 … H) -H #W2 #U2 #HW12 #_ #H destruct
- /2 width=5 by fqu_pair_sn, ex3_2_intro/
-| #p #I #G #L #W1 #U1 #X #H
- elim (tdeq_inv_pair1 … H) -H #W2 #U2 #HW12 #HU12 #H destruct
- /3 width=5 by rdeq_pair_refl, fqu_bind_dx, ex3_2_intro/
-| #p #I #G #L #W1 #U1 #Hb #X #H
- elim (tdeq_inv_pair1 … H) -H #W2 #U2 #HW12 #HU12 #H destruct
- /3 width=5 by fqu_clear, ex3_2_intro/
-| #I #G #L #W1 #U1 #X #H
- elim (tdeq_inv_pair1 … H) -H #W2 #U2 #_ #HU12 #H destruct
- /2 width=5 by fqu_flat_dx, ex3_2_intro/
-| #I #G #L #T1 #U1 #HTU1 #U2 #HU12
- elim (tdeq_inv_lifts_sn … HU12 … HTU1) -U1
- /3 width=5 by fqu_drop, ex3_2_intro/
-]
-qed-.
-
-lemma tdeq_fqu_trans: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, T1⦄ →
- ∀U2. U2 ≛[h, o] U1 →
- ∃∃L,T2. ⦃G1, L1, U2⦄ ⊐[b] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
-#h #o #b #G1 #G2 #L1 #L2 #U1 #T1 #H12 #U2 #HU21
-elim (fqu_tdeq_conf … o … H12 U2) -H12
-/3 width=5 by rdeq_sym, tdeq_sym, ex3_2_intro/
-qed-.
-
-(* Basic_2A1: uses: lleq_fqu_trans *)
-lemma rdeq_fqu_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐[b] ⦃G2, K2, U⦄ →
- ∀L1. L1 ≛[h, o, T] L2 →
- ∃∃K1,U0. ⦃G1, L1, T⦄ ⊐[b] ⦃G2, K1, U0⦄ & U0 ≛[h, o] U & K1 ≛[h, o, U] K2.
-#h #o #b #G1 #G2 #L2 #K2 #T #U #H elim H -G1 -G2 -L2 -K2 -T -U
-[ #I #G #L2 #V2 #L1 #H elim (rdeq_inv_zero_pair_dx … H) -H
- #K1 #V1 #HV1 #HV12 #H destruct
- /3 width=7 by tdeq_rdeq_conf, fqu_lref_O, ex3_2_intro/
-| * [ #p ] #I #G #L2 #V #T #L1 #H
- [ elim (rdeq_inv_bind … H)
- | elim (rdeq_inv_flat … H)
- ] -H
- /2 width=5 by fqu_pair_sn, ex3_2_intro/
-| #p #I #G #L2 #V #T #L1 #H elim (rdeq_inv_bind … H) -H
- /2 width=5 by fqu_bind_dx, ex3_2_intro/
-| #p #I #G #L2 #V #T #Hb #L1 #H elim (rdeq_inv_bind_void … H) -H
- /3 width=5 by fqu_clear, ex3_2_intro/
-| #I #G #L2 #V #T #L1 #H elim (rdeq_inv_flat … H) -H
- /2 width=5 by fqu_flat_dx, ex3_2_intro/
-| #I #G #L2 #T #U #HTU #Y #HU
- elim (rdeq_fwd_dx … HU) #L1 #V1 #H destruct
- /5 width=14 by rdeq_inv_lifts_bi, fqu_drop, drops_refl, drops_drop, ex3_2_intro/
-]
-qed-.
-
-(* Properties with optional structural successor for closures ***************)
-
-lemma tdeq_fquq_trans: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, T1⦄ →
- ∀U2. U2 ≛[h, o] U1 →
- ∃∃L,T2. ⦃G1, L1, U2⦄ ⊐⸮[b] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
-#h #o #b #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -H
-[ #H #U2 #HU21 elim (tdeq_fqu_trans … H … HU21) -U1
- /3 width=5 by fqu_fquq, ex3_2_intro/
-| * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/
-]
-qed-.
-
-(* Basic_2A1: was just: lleq_fquq_trans *)
-lemma rdeq_fquq_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐⸮[b] ⦃G2, K2, U⦄ →
- ∀L1. L1 ≛[h, o, T] L2 →
- ∃∃K1,U0. ⦃G1, L1, T⦄ ⊐⸮[b] ⦃G2, K1, U0⦄ & U0 ≛[h, o] U & K1 ≛[h, o, U] K2.
-#h #o #b #G1 #G2 #L2 #K2 #T #U #H elim H -H
-[ #H #L1 #HL12 elim (rdeq_fqu_trans … H … HL12) -L2 /3 width=5 by fqu_fquq, ex3_2_intro/
-| * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/
-]
-qed-.
-
-(* Properties with plus-iterated structural successor for closures **********)
-
-(* Basic_2A1: was just: lleq_fqup_trans *)
-lemma rdeq_fqup_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐+[b] ⦃G2, K2, U⦄ →
- ∀L1. L1 ≛[h, o, T] L2 →
- ∃∃K1,U0. ⦃G1, L1, T⦄ ⊐+[b] ⦃G2, K1, U0⦄ & U0 ≛[h, o] U & K1 ≛[h, o, U] K2.
-#h #o #b #G1 #G2 #L2 #K2 #T #U #H @(fqup_ind … H) -G2 -K2 -U
-[ #G2 #K2 #U #HTU #L1 #HL12 elim (rdeq_fqu_trans … HTU … HL12) -L2
- /3 width=5 by fqu_fqup, ex3_2_intro/
-| #G #G2 #K #K2 #U #U2 #_ #HU2 #IHTU #L1 #HL12
- elim (IHTU … HL12) -L2 #K0 #U0 #HTU #HU0 #HK0
- elim (rdeq_fqu_trans … HU2 … HK0) -K #K1 #U1 #HU1 #HU12 #HK12
- elim (tdeq_fqu_trans … HU1 … HU0) -U #K3 #U3 #HU03 #HU31 #HK31
- @(ex3_2_intro … K3 U3) (**) (* full auto too slow *)
- /3 width=5 by rdeq_trans, tdeq_rdeq_conf, fqup_strap1, tdeq_trans/
-]
-qed-.
-
-lemma tdeq_fqup_trans: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, T1⦄ →
- ∀U2. U2 ≛[h, o] U1 →
- ∃∃L,T2. ⦃G1, L1, U2⦄ ⊐+[b] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
-#h #o #b #G1 #G2 #L1 #L2 #U1 #T1 #H @(fqup_ind_dx … H) -G1 -L1 -U1
-[ #G1 #L1 #U1 #H #U2 #HU21 elim (tdeq_fqu_trans … H … HU21) -U1
- /3 width=5 by fqu_fqup, ex3_2_intro/
-| #G1 #G #L1 #L #U1 #U #H #_ #IH #U2 #HU21
- elim (tdeq_fqu_trans … H … HU21) -U1 #L0 #T #H1 #HTU #HL0
- lapply (tdeq_rdeq_div … HTU … HL0) -HL0 #HL0
- elim (IH … HTU) -U #K2 #U1 #H2 #HUT1 #HKL2
- elim (rdeq_fqup_trans … H2 … HL0) -L #K #U #H2 #HU1 #HK2
- lapply (tdeq_rdeq_conf … HUT1 … HK2) -HK2 #HK2
- /3 width=7 by rdeq_trans, fqup_strap2, tdeq_trans, ex3_2_intro/
-]
-qed-.
-
-(* Properties with star-iterated structural successor for closures **********)
-
-lemma tdeq_fqus_trans: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, T1⦄ →
- ∀U2. U2 ≛[h, o] U1 →
- ∃∃L,T2. ⦃G1, L1, U2⦄ ⊐*[b] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
-#h #o #b #G1 #G2 #L1 #L2 #U1 #T1 #H #U2 #HU21 elim(fqus_inv_fqup … H) -H
-[ #H elim (tdeq_fqup_trans … H … HU21) -U1 /3 width=5 by fqup_fqus, ex3_2_intro/
-| * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/
-]
-qed-.
-
-(* Basic_2A1: was just: lleq_fqus_trans *)
-lemma rdeq_fqus_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐*[b] ⦃G2, K2, U⦄ →
- ∀L1. L1 ≛[h, o, T] L2 →
- ∃∃K1,U0. ⦃G1, L1, T⦄ ⊐*[b] ⦃G2, K1, U0⦄ & U0 ≛[h, o] U & K1 ≛[h, o, U] K2.
-#h #o #b #G1 #G2 #L2 #K2 #T #U #H #L1 #HL12 elim(fqus_inv_fqup … H) -H
-[ #H elim (rdeq_fqup_trans … H … HL12) -L2 /3 width=5 by fqup_fqus, ex3_2_intro/
-| * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/
-]
-qed-.
projects / helm.git / blobdiff