--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⦃ term 46 L1, break term 46 T1 ⦄ ⊆ ⦃ break term 46 L2, break term 46 T2 ⦄ )"
+ non associative with precedence 45
+ for @{ 'SubSetEq $L1 $T1 $L2 $T2 }.
include "basic_2/rt_transition/cpx_lfxs.ma".
include "basic_2/rt_transition/cpm_cpx.ma".
+include "basic_2/rt_transition/cpr_ext.ma".
(* CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS ***************************)
+(* Properties with context-sensitive free variables *************************)
+
+lemma cpm_frees_conf: ∀n,h,G. R_frees_confluent (cpm n h G).
+/3 width=6 by cpm_fwd_cpx, cpx_frees_conf/ qed-.
+
+lemma lfpr_frees_conf: ∀h,G. lexs_frees_confluent (cpr_ext h G) cfull.
+/5 width=9 by cpm_fwd_cpx, lfpx_frees_conf, lexs_co, cext2_co/ qed-.
+
(* Properties with generic extension on referred entries ********************)
(* Basic_2A1: was just: cpr_llpx_sn_conf *)
(* *)
(**************************************************************************)
-include "basic_2/rt_transition/lfpx_frees.ma".
+include "basic_2/relocation/drops_lexs.ma".
+include "basic_2/static/frees_drops.ma".
+include "basic_2/static/lsubf_frees.ma".
+include "basic_2/static/lfxs.ma".
+include "basic_2/rt_transition/cpx_drops.ma".
+include "basic_2/rt_transition/cpx_ext.ma".
(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************)
+(* Properties with context-sensitive free variables *************************)
+
+(* Basic_2A1: uses: lpx_cpx_frees_trans *)
+lemma cpx_frees_conf_lexs: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
+ ∀L2. L1 ⪤*[cpx_ext h G, cfull, f1] L2 →
+ ∀T2. ⦃G, L1⦄ ⊢ T1 ⬈[h] T2 →
+ ∃∃f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & f2 ⊆ f1.
+#h #G #L1 #T1 @(fqup_wf_ind_eq (Ⓣ) … G L1 T1) -G -L1 -T1
+#G0 #L0 #U0 #IH #G #L1 * *
+[ -IH #s #HG #HL #HU #g1 #H1 #L2 #_ #U2 #H0 destruct
+ lapply (frees_inv_sort … H1) -H1 #Hg1
+ elim (cpx_inv_sort1 … H0) -H0 #H destruct
+ /3 width=3 by frees_sort, sle_refl, ex2_intro/
+| #i #HG #HL #HU #g1 #H1 #L2 #H2 #U2 #H0 destruct
+ elim (frees_inv_lref_drops … H1) -H1 *
+ [ -IH #f1 #HL1 #Hf1 #H destruct
+ elim (cpx_inv_lref1_drops … H0) -H0
+ [ #H destruct
+ /4 width=9 by frees_atom_drops, drops_atom2_lexs_conf, sle_refl, ex2_intro/
+ | * -H2 -Hf1 #I #K1 #V1 #V2 #HLK1
+ lapply (drops_TF … HLK1) -HLK1 #HLK1
+ lapply (drops_mono … HLK1 … HL1) -L1 #H destruct
+ ]
+ | #f1 #I #K1 #V1 #Hf1 #HLK1 #H destruct
+ elim (cpx_inv_lref1_drops … H0) -H0
+ [ #H destruct
+ elim (lexs_drops_conf_next … H2 … HLK1) -H2 [ |*: // ] #Z #K2 #HLK2 #HK12 #H
+ elim (ext2_inv_pair_sn … H) -H #V2 #HV12 #H destruct
+ elim (IH … Hf1 … HK12 … HV12) /2 width=2 by fqup_lref/ -L1 -K1 -V1 #f2 #Hf2 #Hf21
+ /4 width=7 by frees_lref_pushs, frees_pair_drops, drops_refl, sle_pushs, sle_next, ex2_intro/
+ | * #Z #Y #X #V2 #H #HV12 #HVU2
+ lapply (drops_mono … H … HLK1) -H #H destruct
+ elim (lexs_drops_conf_next … H2 … HLK1) -H2 [ |*: // ] #I2 #K2 #HLK2 #HK12 #H
+ elim (ext2_inv_pair_sn … H) -H #V0 #_ #H destruct
+ lapply (drops_isuni_fwd_drop2 … HLK2) // -V0 #HLK2
+ elim (IH … Hf1 … HK12 … HV12) /2 width=2 by fqup_lref/ -I -L1 -K1 -V1 #f2 #Hf2 #Hf21
+ lapply (frees_lifts … Hf2 … HLK2 … HVU2 ??) /4 width=7 by sle_weak, ex2_intro, sle_pushs/
+ ]
+ | #f1 #I #K1 #HLK1 #Hf1 #H destruct
+ elim (cpx_inv_lref1_drops … H0) -H0
+ [ -IH #H destruct
+ elim (lexs_drops_conf_next … H2 … HLK1) -H2 -HLK1 [ |*: // ] #Z #K2 #HLK2 #_ #H
+ lapply (ext2_inv_unit_sn … H) -H #H destruct
+ /3 width=3 by frees_unit_drops, sle_refl, ex2_intro/
+ | * -H2 -Hf1 #Z #Y1 #X1 #X2 #HLY1
+ lapply (drops_mono … HLK1 … HLY1) -L1 #H destruct
+ ]
+ ]
+| -IH #l #HG #HL #HU #g1 #H1 #L2 #_ #U2 #H0 destruct
+ lapply (frees_inv_gref … H1) -H1 #Hg1
+ lapply (cpx_inv_gref1 … H0) -H0 #H destruct
+ /3 width=3 by frees_gref, sle_refl, ex2_intro/
+| #p #I #V1 #T1 #HG #HL #HU #g1 #H1 #L2 #H2 #U2 #H0 destruct
+ elim (frees_inv_bind … H1) -H1 #gV1 #gT1 #HgV1 #HgT1 #Hg1
+ elim (cpx_inv_bind1 … H0) -H0 *
+ [ #V2 #T2 #HV12 #HT12 #H destruct
+ lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V
+ lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
+ lapply (lexs_inv_tl … (BPair I V1) (BPair I V2) … HL12T ??) /2 width=1 by ext2_pair/ -HL12T #HL12T
+ elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21
+ elim (IH … HgT1 … HL12T … HT12) // -IH -HgT1 -HL12T -HT12 #gT2 #HgT2 #HgT21
+ elim (sor_isfin_ex gV2 (⫱gT2)) /3 width=3 by frees_fwd_isfin, isfin_tl/
+ /4 width=10 by frees_bind, monotonic_sle_sor, sle_tl, ex2_intro/
+ | #T2 #HT12 #HUT2 #H0 #H1 destruct -HgV1
+ lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
+ lapply (lexs_inv_tl … (BPair Abbr V1) (BPair Abbr V1) … HL12T ??) /2 width=1 by ext2_pair/ -HL12T #HL12T
+ elim (IH … HgT1 … HL12T … HT12) // -L1 -T1 #gT2 #HgT2 #HgT21
+ lapply (frees_inv_lifts_SO (Ⓣ) … HgT2 … L2 … HUT2) [ /3 width=1 by drops_refl, drops_drop/ ] -V1 -T2
+ /5 width=6 by sor_inv_sle_dx, sle_trans, sle_tl, ex2_intro/
+ ]
+| #I #V1 #T0 #HG #HL #HU #g1 #H1 #L2 #H2 #U2 #H0 destruct
+ elim (frees_inv_flat … H1) -H1 #gV1 #gT0 #HgV1 #HgT0 #Hg1
+ elim (cpx_inv_flat1 … H0) -H0 *
+ [ #V2 #T2 #HV12 #HT12 #H destruct
+ lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V
+ lapply (sle_lexs_trans … H2 gT0 ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
+ elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21
+ elim (IH … HgT0 … HL12T … HT12) // -IH -HgT0 -HL12T -HT12 #gT2 #HgT2 #HgT21
+ elim (sor_isfin_ex gV2 gT2) /2 width=3 by frees_fwd_isfin/
+ /3 width=10 by frees_flat, monotonic_sle_sor, ex2_intro/
+ | #HU2 #H destruct -HgV1
+ lapply (sle_lexs_trans … H2 gT0 ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
+ elim (IH … HgT0 … HL12T … HU2) // -L1 -T0 -V1
+ /4 width=6 by sor_inv_sle_dx, sle_trans, ex2_intro/
+ | #HU2 #H destruct -HgT0
+ lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ -H2 #HL12V
+ elim (IH … HgV1 … HL12V … HU2) // -L1 -T0 -V1
+ /4 width=6 by sor_inv_sle_sn, sle_trans, ex2_intro/
+ | #p #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #HT12 #H0 #H1 #H destruct
+ elim (frees_inv_bind … HgT0) -HgT0 #gW1 #gT1 #HgW1 #HgT1 #HgT0
+ lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V
+ lapply (sle_lexs_trans … H2 gT0 ?) /2 width=2 by sor_inv_sle_dx/ -H2 #H2
+ lapply (sle_lexs_trans … H2 gW1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12W
+ lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
+ lapply (lexs_inv_tl … (BPair Abst W1) (BPair Abst W2) … HL12T ??) /2 width=1 by ext2_pair, I/ -HL12T #HL12T
+ elim (sor_isfin_ex gV1 gW1) /2 width=3 by frees_fwd_isfin/ #g0 #Hg0 #_
+ lapply (sor_assoc_sn … Hg1 … HgT0 … Hg0) -Hg1 -HgT0 #Hg1
+ lapply (sor_comm … Hg0) -Hg0 #Hg0
+ elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21
+ elim (IH … HgW1 … HL12W … HW12) // -HgW1 -HL12W -HW12 #gW2 #HgW2 #HgW21
+ elim (IH … HgT1 … HL12T … HT12) // -IH -HgT1 -HL12T -HT12 #gT2 #HgT2 #HgT21
+ elim (sor_isfin_ex (⫱gT2) gV2) /3 width=3 by frees_fwd_isfin, isfin_tl/ #gVT2 #HgVT2 #_
+ elim (lsubf_beta_tl_dx … HgV2 … HgVT2 … W2) [ |*: /1 width=3 by lsubf_refl/ ] #gT0 #HL2 #HgT02
+ lapply (lsubf_frees_trans … HgT2 … HL2) -HgT2 -HL2 #HgT0
+ lapply (sor_comm … HgVT2) -HgVT2 #HgVT2 (**) (* this should be removed *)
+ elim (sor_isfin_ex gW2 gV2) /2 width=3 by frees_fwd_isfin/ #gV0 #HgV0 #H
+ elim (sor_isfin_ex gV0 (⫱gT0)) /3 width=3 by frees_fwd_isfin, isfin_tl/ -H #g2 #Hg2 #_
+ @(ex2_intro … g2) /3 width=5 by frees_flat, frees_bind/ -h -p -G -L1 -L2 -V1 -V2 -W1 -W2 -T1 -T2
+ @(sor_inv_sle … Hg2) -Hg2
+ [ /3 width=11 by sor_inv_sle_sn_trans, monotonic_sle_sor/
+ | @(sle_trans … HgT02) -HgT02
+ /3 width=8 by monotonic_sle_sor, sor_inv_sle_dx_trans, sle_tl/
+ ] (**) (* full auto too slow *)
+ | #p #V2 #V #W1 #W2 #T1 #T2 #HV12 #HV2 #HW12 #HT12 #H0 #H1 #H destruct
+ elim (frees_inv_bind … HgT0) -HgT0 #gW1 #gT1 #HgW1 #HgT1 #HgT0
+ lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V
+ lapply (sle_lexs_trans … H2 gT0 ?) /2 width=2 by sor_inv_sle_dx/ -H2 #H2
+ lapply (sle_lexs_trans … H2 gW1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12W
+ lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
+ lapply (lexs_inv_tl … (BPair Abbr W1) (BPair Abbr W2) … HL12T ??) /2 width=1 by ext2_pair, I/ -HL12T #HL12T
+ elim (sor_isfin_ex gV1 gW1) /2 width=3 by frees_fwd_isfin/ #g0 #Hg0 #_
+ lapply (sor_assoc_sn … Hg1 … HgT0 … Hg0) -Hg1 -HgT0 #Hg1
+ elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21
+ elim (IH … HgW1 … HL12W … HW12) // -HgW1 -HL12W -HW12 #gW2 #HgW2 #HgW21
+ elim (IH … HgT1 … HL12T … HT12) // -IH -HgT1 -HL12T -HT12 #gT2 #HgT2 #HgT21
+ elim (sor_isfin_ex (↑gV2) gT2) /3 width=3 by frees_fwd_isfin, isfin_push/ #gV0 #HgV0 #H
+ elim (sor_isfin_ex gW2 (⫱gV0)) /3 width=3 by frees_fwd_isfin, isfin_tl/ -H #g2 #Hg2 #_
+ elim (sor_isfin_ex gW2 gV2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
+ lapply (sor_assoc_sn … Hg2 … (⫱gT2) … Hg) /2 width=1 by sor_tl/ #Hg2
+ lapply (frees_lifts (Ⓣ) … HgV2 … (L2.ⓓW2) … HV2 ??)
+ [4: lapply (sor_comm … Hg) |*: /3 width=3 by drops_refl, drops_drop/ ] -V2 (**) (* full auto too slow *)
+ /4 width=10 by frees_flat, frees_bind, monotonic_sle_sor, sle_tl, ex2_intro/
+ ]
+]
+qed-.
+
+(* Basic_2A1: uses: cpx_frees_trans *)
+lemma cpx_frees_conf: ∀h,G. R_frees_confluent (cpx h G).
+/4 width=7 by cpx_frees_conf_lexs, lexs_refl, ext2_refl/ qed-.
+
+(* Basic_2A1: uses: lpx_frees_trans *)
+lemma lfpx_frees_conf: ∀h,G. lexs_frees_confluent (cpx_ext h G) cfull.
+/2 width=7 by cpx_frees_conf_lexs/ qed-.
+
(* Properties with generic extension on referred entries ********************)
(* Note: lemma 1000 *)
-(* Basic_2A1: was just: cpx_llpx_sn_conf *)
+(* Basic_2A1: uses: cpx_llpx_sn_conf *)
lemma cpx_lfxs_conf: ∀R,h,G. s_r_confluent1 … (cpx h G) (lfxs R).
#R #h #G #L1 #T1 #T2 #H #L2 * #f1 #Hf1 elim (cpx_frees_conf … Hf1 … H) -T1
/3 width=5 by sle_lexs_trans, ex2_intro/
+++ /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/rt_transition/lfpx_frees.ma".
-include "basic_2/rt_transition/cpm_cpx.ma".
-include "basic_2/rt_transition/cpr_ext.ma".
-
-(* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************)
-
-(* Properties with context-sensitive free variables *************************)
-
-lemma cpm_frees_conf: ∀n,h,G. R_frees_confluent (cpm n h G).
-/3 width=6 by cpm_fwd_cpx, cpx_frees_conf/ qed-.
-
-lemma lfpr_frees_conf: ∀h,G. lexs_frees_confluent (cpr_ext h G) cfull.
-/5 width=9 by cpm_fwd_cpx, lfpx_frees_conf, lexs_co, cext2_co/ qed-.
include "basic_2/static/lfxs_lfxs.ma".
include "basic_2/rt_transition/cpm_lsubr.ma".
+include "basic_2/rt_transition/cpm_lfxs.ma".
include "basic_2/rt_transition/cpr.ma".
include "basic_2/rt_transition/cpr_drops.ma".
include "basic_2/rt_transition/lfpr_drops.ma".
include "basic_2/rt_transition/lfpr_fqup.ma".
-include "basic_2/rt_transition/lfpr_frees.ma".
(* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************)
+++ /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/relocation/drops_lexs.ma".
-include "basic_2/static/frees_drops.ma".
-include "basic_2/static/lsubf_frees.ma".
-include "basic_2/static/lfxs.ma".
-include "basic_2/rt_transition/cpx_drops.ma".
-include "basic_2/rt_transition/cpx_ext.ma".
-
-(* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****)
-
-(* Properties with context-sensitive free variables *************************)
-
-(* Basic_2A1: uses: lpx_cpx_frees_trans *)
-(* check sle_refl *)
-lemma cpx_frees_conf_lfpx: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
- ∀L2. L1 ⪤*[cpx_ext h G, cfull, f1] L2 →
- ∀T2. ⦃G, L1⦄ ⊢ T1 ⬈[h] T2 →
- ∃∃f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & f2 ⊆ f1.
-#h #G #L1 #T1 @(fqup_wf_ind_eq (Ⓣ) … G L1 T1) -G -L1 -T1
-#G0 #L0 #U0 #IH #G #L1 * *
-[ -IH #s #HG #HL #HU #g1 #H1 #L2 #_ #U2 #H0 destruct
- lapply (frees_inv_sort … H1) -H1 #Hg1
- elim (cpx_inv_sort1 … H0) -H0 #H destruct
- /3 width=3 by frees_sort, sle_refl, ex2_intro/
-| #i #HG #HL #HU #g1 #H1 #L2 #H2 #U2 #H0 destruct
- elim (frees_inv_lref_drops … H1) -H1 *
- [ -IH #f1 #HL1 #Hf1 #H destruct
- elim (cpx_inv_lref1_drops … H0) -H0
- [ #H destruct
- /4 width=9 by frees_atom_drops, drops_atom2_lexs_conf, sle_refl, ex2_intro/
- | * -H2 -Hf1 #I #K1 #V1 #V2 #HLK1
- lapply (drops_TF … HLK1) -HLK1 #HLK1
- lapply (drops_mono … HLK1 … HL1) -L1 #H destruct
- ]
- | #f1 #I #K1 #V1 #Hf1 #HLK1 #H destruct
- elim (cpx_inv_lref1_drops … H0) -H0
- [ #H destruct
- elim (lexs_drops_conf_next … H2 … HLK1) -H2 [ |*: // ] #Z #K2 #HLK2 #HK12 #H
- elim (ext2_inv_pair_sn … H) -H #V2 #HV12 #H destruct
- elim (IH … Hf1 … HK12 … HV12) /2 width=2 by fqup_lref/ -L1 -K1 -V1 #f2 #Hf2 #Hf21
- /4 width=7 by frees_lref_pushs, frees_pair_drops, drops_refl, sle_pushs, sle_next, ex2_intro/
- | * #Z #Y #X #V2 #H #HV12 #HVU2
- lapply (drops_mono … H … HLK1) -H #H destruct
- elim (lexs_drops_conf_next … H2 … HLK1) -H2 [ |*: // ] #I2 #K2 #HLK2 #HK12 #H
- elim (ext2_inv_pair_sn … H) -H #V0 #_ #H destruct
- lapply (drops_isuni_fwd_drop2 … HLK2) // -V0 #HLK2
- elim (IH … Hf1 … HK12 … HV12) /2 width=2 by fqup_lref/ -I -L1 -K1 -V1 #f2 #Hf2 #Hf21
- lapply (frees_lifts … Hf2 … HLK2 … HVU2 ??) /4 width=7 by sle_weak, ex2_intro, sle_pushs/
- ]
- | #f1 #I #K1 #HLK1 #Hf1 #H destruct
- elim (cpx_inv_lref1_drops … H0) -H0
- [ -IH #H destruct
- elim (lexs_drops_conf_next … H2 … HLK1) -H2 -HLK1 [ |*: // ] #Z #K2 #HLK2 #_ #H
- lapply (ext2_inv_unit_sn … H) -H #H destruct
- /3 width=3 by frees_unit_drops, sle_refl, ex2_intro/
- | * -H2 -Hf1 #Z #Y1 #X1 #X2 #HLY1
- lapply (drops_mono … HLK1 … HLY1) -L1 #H destruct
- ]
- ]
-| -IH #l #HG #HL #HU #g1 #H1 #L2 #_ #U2 #H0 destruct
- lapply (frees_inv_gref … H1) -H1 #Hg1
- lapply (cpx_inv_gref1 … H0) -H0 #H destruct
- /3 width=3 by frees_gref, sle_refl, ex2_intro/
-| #p #I #V1 #T1 #HG #HL #HU #g1 #H1 #L2 #H2 #U2 #H0 destruct
- elim (frees_inv_bind … H1) -H1 #gV1 #gT1 #HgV1 #HgT1 #Hg1
- elim (cpx_inv_bind1 … H0) -H0 *
- [ #V2 #T2 #HV12 #HT12 #H destruct
- lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V
- lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
- lapply (lexs_inv_tl … (BPair I V1) (BPair I V2) … HL12T ??) /2 width=1 by ext2_pair/ -HL12T #HL12T
- elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21
- elim (IH … HgT1 … HL12T … HT12) // -IH -HgT1 -HL12T -HT12 #gT2 #HgT2 #HgT21
- elim (sor_isfin_ex gV2 (⫱gT2)) /3 width=3 by frees_fwd_isfin, isfin_tl/
- /4 width=10 by frees_bind, monotonic_sle_sor, sle_tl, ex2_intro/
- | #T2 #HT12 #HUT2 #H0 #H1 destruct -HgV1
- lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
- lapply (lexs_inv_tl … (BPair Abbr V1) (BPair Abbr V1) … HL12T ??) /2 width=1 by ext2_pair/ -HL12T #HL12T
- elim (IH … HgT1 … HL12T … HT12) // -L1 -T1 #gT2 #HgT2 #HgT21
- lapply (frees_inv_lifts_SO (Ⓣ) … HgT2 … L2 … HUT2) [ /3 width=1 by drops_refl, drops_drop/ ] -V1 -T2
- /5 width=6 by sor_inv_sle_dx, sle_trans, sle_tl, ex2_intro/
- ]
-| #I #V1 #T0 #HG #HL #HU #g1 #H1 #L2 #H2 #U2 #H0 destruct
- elim (frees_inv_flat … H1) -H1 #gV1 #gT0 #HgV1 #HgT0 #Hg1
- elim (cpx_inv_flat1 … H0) -H0 *
- [ #V2 #T2 #HV12 #HT12 #H destruct
- lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V
- lapply (sle_lexs_trans … H2 gT0 ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
- elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21
- elim (IH … HgT0 … HL12T … HT12) // -IH -HgT0 -HL12T -HT12 #gT2 #HgT2 #HgT21
- elim (sor_isfin_ex gV2 gT2) /2 width=3 by frees_fwd_isfin/
- /3 width=10 by frees_flat, monotonic_sle_sor, ex2_intro/
- | #HU2 #H destruct -HgV1
- lapply (sle_lexs_trans … H2 gT0 ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
- elim (IH … HgT0 … HL12T … HU2) // -L1 -T0 -V1
- /4 width=6 by sor_inv_sle_dx, sle_trans, ex2_intro/
- | #HU2 #H destruct -HgT0
- lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ -H2 #HL12V
- elim (IH … HgV1 … HL12V … HU2) // -L1 -T0 -V1
- /4 width=6 by sor_inv_sle_sn, sle_trans, ex2_intro/
- | #p #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #HT12 #H0 #H1 #H destruct
- elim (frees_inv_bind … HgT0) -HgT0 #gW1 #gT1 #HgW1 #HgT1 #HgT0
- lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V
- lapply (sle_lexs_trans … H2 gT0 ?) /2 width=2 by sor_inv_sle_dx/ -H2 #H2
- lapply (sle_lexs_trans … H2 gW1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12W
- lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
- lapply (lexs_inv_tl … (BPair Abst W1) (BPair Abst W2) … HL12T ??) /2 width=1 by ext2_pair, I/ -HL12T #HL12T
- elim (sor_isfin_ex gV1 gW1) /2 width=3 by frees_fwd_isfin/ #g0 #Hg0 #_
- lapply (sor_assoc_sn … Hg1 … HgT0 … Hg0) -Hg1 -HgT0 #Hg1
- lapply (sor_comm … Hg0) -Hg0 #Hg0
- elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21
- elim (IH … HgW1 … HL12W … HW12) // -HgW1 -HL12W -HW12 #gW2 #HgW2 #HgW21
- elim (IH … HgT1 … HL12T … HT12) // -IH -HgT1 -HL12T -HT12 #gT2 #HgT2 #HgT21
- elim (sor_isfin_ex (⫱gT2) gV2) /3 width=3 by frees_fwd_isfin, isfin_tl/ #gVT2 #HgVT2 #_
- elim (lsubf_beta_tl_dx … HgV2 … HgVT2 … W2) [ |*: /1 width=3 by lsubf_refl/ ] #gT0 #HL2 #HgT02
- lapply (lsubf_frees_trans … HgT2 … HL2) -HgT2 -HL2 #HgT0
- lapply (sor_comm … HgVT2) -HgVT2 #HgVT2 (**) (* this should be removed *)
- elim (sor_isfin_ex gW2 gV2) /2 width=3 by frees_fwd_isfin/ #gV0 #HgV0 #H
- elim (sor_isfin_ex gV0 (⫱gT0)) /3 width=3 by frees_fwd_isfin, isfin_tl/ -H #g2 #Hg2 #_
- @(ex2_intro … g2) /3 width=5 by frees_flat, frees_bind/ -h -p -G -L1 -L2 -V1 -V2 -W1 -W2 -T1 -T2
- @(sor_inv_sle … Hg2) -Hg2
- [ /3 width=11 by sor_inv_sle_sn_trans, monotonic_sle_sor/
- | @(sle_trans … HgT02) -HgT02
- /3 width=8 by monotonic_sle_sor, sor_inv_sle_dx_trans, sle_tl/
- ] (**) (* full auto too slow *)
- | #p #V2 #V #W1 #W2 #T1 #T2 #HV12 #HV2 #HW12 #HT12 #H0 #H1 #H destruct
- elim (frees_inv_bind … HgT0) -HgT0 #gW1 #gT1 #HgW1 #HgT1 #HgT0
- lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V
- lapply (sle_lexs_trans … H2 gT0 ?) /2 width=2 by sor_inv_sle_dx/ -H2 #H2
- lapply (sle_lexs_trans … H2 gW1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12W
- lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
- lapply (lexs_inv_tl … (BPair Abbr W1) (BPair Abbr W2) … HL12T ??) /2 width=1 by ext2_pair, I/ -HL12T #HL12T
- elim (sor_isfin_ex gV1 gW1) /2 width=3 by frees_fwd_isfin/ #g0 #Hg0 #_
- lapply (sor_assoc_sn … Hg1 … HgT0 … Hg0) -Hg1 -HgT0 #Hg1
- elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21
- elim (IH … HgW1 … HL12W … HW12) // -HgW1 -HL12W -HW12 #gW2 #HgW2 #HgW21
- elim (IH … HgT1 … HL12T … HT12) // -IH -HgT1 -HL12T -HT12 #gT2 #HgT2 #HgT21
- elim (sor_isfin_ex (↑gV2) gT2) /3 width=3 by frees_fwd_isfin, isfin_push/ #gV0 #HgV0 #H
- elim (sor_isfin_ex gW2 (⫱gV0)) /3 width=3 by frees_fwd_isfin, isfin_tl/ -H #g2 #Hg2 #_
- elim (sor_isfin_ex gW2 gV2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
- lapply (sor_assoc_sn … Hg2 … (⫱gT2) … Hg) /2 width=1 by sor_tl/ #Hg2
- lapply (frees_lifts (Ⓣ) … HgV2 … (L2.ⓓW2) … HV2 ??)
- [4: lapply (sor_comm … Hg) |*: /3 width=3 by drops_refl, drops_drop/ ] -V2 (**) (* full auto too slow *)
- /4 width=10 by frees_flat, frees_bind, monotonic_sle_sor, sle_tl, ex2_intro/
- ]
-]
-qed-.
-
-(* Basic_2A1: uses: cpx_frees_trans *)
-lemma cpx_frees_conf: ∀h,G. R_frees_confluent (cpx h G).
-/4 width=7 by cpx_frees_conf_lfpx, lexs_refl, ext2_refl/ qed-.
-
-(* Basic_2A1: uses: lpx_frees_trans *)
-lemma lfpx_frees_conf: ∀h,G. lexs_frees_confluent (cpx_ext h G) cfull.
-/2 width=7 by cpx_frees_conf_lfpx/ qed-.
include "basic_2/relocation/lifts_tdeq.ma".
include "basic_2/static/lfxs_lfxs.ma".
include "basic_2/static/lfdeq_fqup.ma".
-include "basic_2/rt_transition/lfpx_frees.ma".
-include "basic_2/rt_transition/lfpx.ma". (**) (* should be in lfpx_frees.ma *)
+include "basic_2/rt_transition/cpx_lfxs.ma".
+include "basic_2/rt_transition/lfpx.ma".
(* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****)
--- /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 "ground_2/relocation/rtmap_id.ma".
+include "basic_2/notation/relations/subseteq_4.ma".
+include "basic_2/static/frees.ma".
+
+(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
+
+definition fle: bi_relation lenv term ≝ λL1,T1,L2,T2.
+ ∃∃f1,f2. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 & L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & f1 ⊆ f2.
+
+interpretation "free variables inclusion (restricted closure)"
+ 'SubSetEq L1 T1 L2 T2 = (fle L1 T1 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fle_sort: ∀L1,L2,s1,s2. ⦃L1, ⋆s1⦄ ⊆ ⦃L2, ⋆s2⦄.
+/3 width=5 by frees_sort, sle_refl, ex3_2_intro/ qed.
+
+lemma fle_gref: ∀L1,L2,l1,l2. ⦃L1, §l1⦄ ⊆ ⦃L2, §l2⦄.
+/3 width=5 by frees_gref, sle_refl, ex3_2_intro/ qed.
+
+lemma fle_bind: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
+ ∀I1,I2,T1,T2. ⦃L1.ⓑ{I1}V1, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄ →
+ ∀p. ⦃L1, ⓑ{p,I1}V1.T1⦄ ⊆ ⦃L2, ⓑ{p,I2}V2.T2⦄.
+#L1 #L2 #V1 #V2 * #f1 #g1 #HV1 #HV2 #Hfg1 #I1 #I2 #T1 #T2 * #f2 #g2 #Hf2 #Hg2 #Hfg2 #p
+elim (sor_isfin_ex f1 (⫱f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
+elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+/4 width=12 by frees_bind, monotonic_sle_sor, sle_tl, ex3_2_intro/
+qed.
+
+lemma fle_flat: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ⊆ ⦃L2, V2⦄ →
+ ∀T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
+ ∀I1,I2. ⦃L1, ⓕ{I1}V1.T1⦄ ⊆ ⦃L2, ⓕ{I2}V2.T2⦄.
+#L1 #L2 #V1 #V2 * #f1 #g1 #HV1 #HV2 #Hfg1 #T1 #T2 * #f2 #g2 #Hf2 #Hg2 #Hfg2 #I1 #I2
+elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
+elim (sor_isfin_ex g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
+/3 width=12 by frees_flat, monotonic_sle_sor, ex3_2_intro/
+qed.
--- /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/static/frees_drops.ma".
+include "basic_2/static/fle.ma".
+
+(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
+
+(* Advanced properties ******************************************************)
+
+lemma fle_bind_dx: ∀T,U. ⬆*[1] T ≡ U →
+ ∀p,I,L,V. ⦃L, T⦄ ⊆ ⦃L, ⓑ{p,I}V.U⦄.
+#T #U #HTU #p #I #L #V
+elim (frees_total L V) #f1 #Hf1
+elim (frees_total L T) #f2 #Hf2
+elim (sor_isfin_ex f1 f2) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #H #_
+lapply (sor_inv_sle_dx … H) #Hf0
+>(tl_push_rew f) in H; #Hf
+/6 width=6 by frees_lifts_SO, frees_bind, drops_refl, drops_drop, ex3_2_intro/
+qed.
--- /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/static/frees_frees.ma".
+include "basic_2/static/fle.ma".
+
+(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
+
+(* Main properties **********************************************************)
+
+theorem fle_trans: bi_transitive … fle.
+#L1 #L #T1 #T * #f1 #f #HT1 #HT #Hf1 #L2 #T2 * #g #f2 #Hg #HT2 #Hf2
+/5 width=8 by frees_mono, sle_trans, sle_eq_repl_back2, ex3_2_intro/
+qed-.
--- /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/static/frees_fqup.ma".
+include "basic_2/static/fle.ma".
+
+(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
+
+(* Advanced properties ******************************************************)
+
+lemma fle_refl: bi_reflexive … fle.
+#L #T elim (frees_total L T) /2 width=5 by sle_refl, ex3_2_intro/
+qed.
+
+lemma fle_bind_sn: ∀p,I,L,V,T. ⦃L, V⦄ ⊆ ⦃L, ⓑ{p,I}V.T⦄.
+#p #I #L #V #T
+elim (frees_total L V) #f1 #Hf1
+elim (frees_total (L.ⓑ{I}V) T) #f2 #Hf2
+elim (sor_isfin_ex f1 (⫱f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
+/3 width=6 by frees_bind, sor_inv_sle_sn, ex3_2_intro/
+qed.
+
+lemma fle_flat_sn: ∀I,L,V,T. ⦃L, V⦄ ⊆ ⦃L, ⓕ{I}V.T⦄.
+#I #L #V #T
+elim (frees_total L V) #f1 #Hf1
+elim (frees_total L T) #f2 #Hf2
+elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
+/3 width=6 by frees_flat, sor_inv_sle_sn, ex3_2_intro/
+qed.
+
+lemma fle_flat_dx: ∀I,L,V,T. ⦃L, T⦄ ⊆ ⦃L, ⓕ{I}V.T⦄.
+#I #L #V #T
+elim (frees_total L V) #f1 #Hf1
+elim (frees_total L T) #f2 #Hf2
+elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
+/3 width=6 by frees_flat, sor_inv_sle_dx, ex3_2_intro/
+qed.
]
qed-.
+lemma frees_lifts_SO: ∀b,L,K. ⬇*[b, 𝐔❴1❵] L ≡ K → ∀T,U. ⬆*[1] T ≡ U →
+ ∀f. K ⊢ 𝐅*⦃T⦄ ≡ f → L ⊢ 𝐅*⦃U⦄ ≡ ↑f.
+#b #L #K #HLK #T #U #HTU #f #Hf
+@(frees_lifts b … Hf … HTU) // (**) (* auto fails *)
+qed.
+
(* Forward lemmas with generic slicing for local environments ***************)
lemma frees_fwd_coafter: ∀b,f2,L,U. L ⊢ 𝐅*⦃U⦄ ≡ f2 →
--- /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/static/frees_frees.ma".
+include "basic_2/static/fle.ma".
+include "basic_2/static/lfxs_lfxs.ma".
+
+(* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
+
+(* Properties with free variables inclusion for restricted closures *********)
+
+lemma fle_lfxs_trans: ∀R,L1,T1,T2. ⦃L1, T1⦄ ⊆ ⦃L1, T2⦄ →
+ ∀L2. L1 ⪤*[R, T2] L2 → L1 ⪤*[R, T1] L2.
+#R #L1 #T1 #T2 * #f1 #f2 #Hf1 #Hf2 #Hf12 #L2 #HL12
+/4 width=5 by lfxs_inv_frees, sle_lexs_trans, ex2_intro/
+qed-.
--- /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/relocation/lex.ma".
+include "basic_2/static/lfxs_fqup.ma".
+
+(* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
+
+(* Properties with generic extension of a context-sensitive relation ********)
+
+lemma lfxs_lex: ∀R,L1,L2. L1 ⪤[R] L2 → ∀T. L1 ⪤*[R, T] L2.
+#R #L1 #L2 * #f #Hf #HL12 #T
+elim (frees_total L1 T) #g #Hg
+/4 width=5 by lexs_sdj, sdj_isid_sn, ex2_intro/
+qed.
}
]
[ { "context-sensitive parallel r-transition" * } {
- [ [ "for lenvs on referred entries" ] "lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lfpr_length" + "lfpr_drops" + "lfpr_fquq" + "lfpr_fqup" + "lfpr_frees" + "lfpr_aaa" + "lfpr_lfpx" + "lfpr_lfpr" * ]
+ [ [ "for lenvs on referred entries" ] "lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lfpr_length" + "lfpr_drops" + "lfpr_fquq" + "lfpr_fqup" + "lfpr_aaa" + "lfpr_lfpx" + "lfpr_lfpr" * ]
[ [ "for binders" ] "cpr_ext ( ⦃?,?⦄ ⊢ ? ➡[?] ? )" * ]
[ [ "for terms" ] "cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )" "cpr_drops" * ]
}
]
[ { "uncounted context-sensitive parallel rt-transition" * } {
[ [ "normal form for terms" ] "cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )" "cnx_simple" + "cnx_drops" + "cnx_cnx" * ]
- [ [ "for lenvs on referred entries" ] "lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )" "lfpx_length" + "lfpx_drops" + "lfpx_fqup" + "lfpx_frees" + "lfpx_lfdeq" + "lfpx_aaa" + "lfpx_cpx" + "lfpx_lfpx" * ]
+ [ [ "for lenvs on referred entries" ] "lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )" "lfpx_length" + "lfpx_drops" + "lfpx_fqup" + "lfpx_lfdeq" + "lfpx_aaa" + "lfpx_cpx" + "lfpx_lfpx" * ]
[ [ "for lenvs on all entries" ] "lpx ( ⦃?,?⦄ ⊢ ⬈[?] ? )" * ]
[ [ "for binders" ] "cpx_ext ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" * ]
[ [ "for terms" ] "cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" "cpx_simple" + "cpx_drops" + "cpx_fqus" + "cpx_lsubr" + "cpx_lfxs" + "cpx_lfeq" * ]
}
]
[ { "generic extension of a context-sensitive relation" * } {
- [ [ "for lenvs on referred entries" ] "lfxs ( ? ⦻*[?,?] ? )" "lfxs_length" + "lfxs_drops" + "lfxs_fqup" + "lfxs_lfxs" * ]
+ [ [ "for lenvs on referred entries" ] "lfxs ( ? ⦻*[?,?] ? )" "lfxs_length" + "lfxs_lex" + "lfxs_drops" + "lfxs_fqup" + "flxs_fle" + "lfxs_lfxs" * ]
}
]
[ { "context-sensitive free variables" * } {
+ [ [ "inclusion for restricted closures" ] "fle ( ⦃?,?⦄ ⊆ ⦃?,?⦄ )" "fle_drops" + "fle_fqup" + "fle_fle" * ]
[ [ "restricted refinement for lenvs" ] "lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )" "lsubf_lsubr" + "lsubf_frees" + "lsubf_lsubf" * ]
[ [ "for terms" ] "frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )" "frees_drops" + "frees_fqup" + "frees_frees" * ]
}
projects / helm.git / commitdiff