From: Ferruccio Guidi Date: Wed, 14 Mar 2018 14:53:37 +0000 (+0100) Subject: update in basic_2 X-Git-Tag: make_still_working~353 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=c6305166703a17801bbd08a85fe93ef4abf8ff85;p=helm.git update in basic_2 + advances on fpbq + minor updates --- diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/fpbq/fpbq_alt.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/fpbq/fpbq_alt.etc deleted file mode 100644 index 2607572d6..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/etc/fpbq/fpbq_alt.etc +++ /dev/null @@ -1,53 +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/notation/relations/btpredalt_8.ma". -include "basic_2/reduction/fpb_fleq.ma". -include "basic_2/reduction/fpbq.ma". - -(* "QRST" PARALLEL REDUCTION FOR CLOSURES ***********************************) - -(* Basic properties *********************************************************) - -lemma fleq_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2. - ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=1 by fpbq_lleq/ -qed. - -lemma fpb_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → - ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 -/3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lpx, fqu_fquq/ -qed. - -(* Advanced eliminators *****************************************************) - -lemma fpbq_ind_alt: ∀h,o,G1,G2,L1,L2,T1,T2. ∀R:Prop. - (⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → R) → - (⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R) → - ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ → R. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #R #HI1 #HI2 #H elim (fpbq_fpbqa … H) /2 width=1 by/ -qed-. - -(* aternative definition of fpb *********************************************) - -lemma fpb_fpbq_alt: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → - ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ ∧ (⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⊥). -/3 width=10 by fpb_fpbq, fpb_inv_fleq, conj/ qed. - -lemma fpbq_inv_fpb_alt: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ → - (⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⊥) → ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #H0 @(fpbq_ind_alt … H) -H // -#H elim H0 -H0 // -qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/fsle.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/fsle.etc new file mode 100644 index 000000000..9e94c20bc --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/etc/fsle.etc @@ -0,0 +1,31 @@ +(**************************************************************************) +(* ___ *) +(* ||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/lsubr_length.ma". +include "basic_2/rt_transition/lfpx_fsle.ma". + +lemma pippo: ∀L1,L2. L2 ⫃ L1 → ∀T. ⦃L1, T⦄ ⊆ ⦃L2, T⦄. +#L1 #L2 #HL #T +elim (frees_total L1 T) #f1 #Hf1 +elim (frees_total L2 T) #f2 #Hf2 +lapply (lsubr_lsubf … Hf1 … HL … Hf2) #H +lapply (lsubf_fwd_sle … H) -H #H12 +lapply (lsubr_fwd_length … HL) -HL #HL +/3 width=8 by lveq_length_eq, ex4_4_intro/ +qed. + +lemma R_fle_comp_LTC: ∀R. R_fle_compatible R → R_fle_compatible (LTC … R). +#R #HR #L #T1 #T2 #H elim H -T2 +/3 width=3 by fle_trans_dx/ +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq.ma index 869f3e118..08c3d16db 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq.ma @@ -19,12 +19,12 @@ include "basic_2/rt_transition/lfpr_lfpx.ma". (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************) -(* Basic_2A1: includes: fpbq_lleq *) +(* Basic_2A1: includes: fleq_fpbq fpbq_lleq *) inductive fpbq (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝ | fpbq_fquq : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpbq h o G1 L1 T1 G2 L2 T2 | fpbq_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → fpbq h o G1 L1 T1 G1 L1 T2 | fpbq_lfpx : ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → fpbq h o G1 L1 T1 G1 L2 T1 -| ffpq_lfdeq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → fpbq h o G1 L1 T1 G2 L2 T2 +| fpbq_ffdeq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → fpbq h o G1 L1 T1 G2 L2 T2 . interpretation diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_fpb.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_fpb.ma new file mode 100644 index 000000000..ac20a6259 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_fpb.ma @@ -0,0 +1,55 @@ +(**************************************************************************) +(* ___ *) +(* ||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/fpb_ffdeq.ma". +include "basic_2/rt_transition/fpbq.ma". + +(* PARALLEL RST-TRANSITION FOR CLOSURES *************************************) + +(* Properties with proper parallel rst-transition for closures **************) + +lemma fpb_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → + ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄. +#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 +/3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lfpx, fqu_fquq/ +qed. + +(* Basic_2A1: fpb_fpbq_alt *) +lemma fpb_fpbq_ffdneq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → + ∧∧ ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ & (⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥). +/3 width=10 by fpb_fpbq, fpb_inv_ffdeq, conj/ qed-. + +(* Inversrion lemmas with proper parallel rst-transition for closures *******) + +(* Basic_2A1: uses: fpbq_ind_alt *) +lemma fpbq_inv_fpb: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ → + ∨∨ ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ + | ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄. +#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 +[ #G2 #L2 #T2 * [2: * #H1 #H2 #H3 destruct ] + /3 width=1 by fpb_fqu, ffdeq_intro_sn, or_intror, or_introl/ +| #T2 #H elim (tdeq_dec h o T1 T2) + /4 width=1 by fpb_cpx, ffdeq_intro_sn, or_intror, or_introl/ +| #L2 elim (lfdeq_dec h o L1 L2 T1) + /4 width=1 by fpb_lfpx, ffdeq_intro_sn, or_intror, or_introl/ +| /2 width=1 by or_introl/ +] +qed-. + +(* Basic_2A1: fpbq_inv_fpb_alt *) +lemma fpbq_ffdneq_inv_fpb: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ → + (⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥) → ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄. +#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #H0 +elim (fpbq_inv_fpb … H) -H // #H elim H0 -H0 // +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_etc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_etc.ma deleted file mode 100644 index 7d5523fe3..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_etc.ma +++ /dev/null @@ -1,123 +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/rt_transition/lfpx_fsle.ma". -(* -lemma R_fle_comp_LTC: ∀R. R_fle_compatible R → R_fle_compatible (LTC … R). -#R #HR #L #T1 #T2 #H elim H -T2 -/3 width=3 by fle_trans_dx/ -qed-. -*) - -(* Note: "⦃L2, T1⦄ ⊆ ⦃L0, T1⦄" may not hold *) -axiom lfpx_cpx_conf_fsle4: ∀h,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 → - ∀L2. ⦃G, L0⦄ ⊢⬈[h, T0] L2 → ⦃L2, T1⦄ ⊆ ⦃L0, T1⦄. -(* -#h #G0 #L0 #T0 @(fqup_wf_ind_eq (Ⓕ) … G0 L0 T0) -G0 -L0 -T0 -#G #L #T #IH #G0 #L0 * * -[ #s #HG #HL #HT #X #HX #Y #HY destruct -IH - lapply (lfxs_fwd_length … HY) -HY #H0 - elim (cpx_inv_sort1 … HX) -HX #H destruct - /3 width=1 by fsle_sort_length, and3_intro/ -| * [| #i ] #HG #HL #HT #X #HX #Y #HY destruct - [ elim (cpx_inv_zero1 … HX) -HX - [ #H destruct - elim (lfxs_inv_zero … HY) -HY * - [ #H1 #H2 destruct -IH /2 width=1 by and3_intro/ - | #I #K0 #K2 #V0 #V2 #HK02 #HV02 #H1 #H2 destruct - lapply (lfxs_fwd_length … HK02) #HK - elim H2R -H2R #H2R - [ <(H2R G0) in HV02; -H2R #HV02 - elim (IH … HV02 … HK02) /2 width=2 by fqu_fqup, fqu_lref_O/ -IH -HV02 -HK02 #H1V #H2V #_ - /4 width=1 by fsle_trans_tc, fsle_zero_bi, and3_intro/ - | lapply (H2R … HV02 … HK02) -H2R -HV02 -HK02 -IH #HKV20 - /3 width=1 by fsle_zero_bi, and3_intro/ - ] - | #f #I #K0 #K2 #Hf #HK02 #H1 #H2 destruct - ] - | * #I0 #K0 #V0 #V1 #HV01 #HV1X #H destruct - elim (lfxs_inv_zero_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct - ] - | elim (cpx_inv_lref1 … HX) -HX - [ #H destruct - elim (lfxs_inv_lref … HY) -HY * - [ #H0 #H1 destruct /2 width=1 by and3_intro/ - | #I0 #I2 #K0 #K2 #HK02 #H1 #H2 destruct - lapply (lfxs_fwd_length … HK02) #HK - elim (IH … HK02) [|*: /2 width=4 by fqu_fqup/ ] -IH -HK02 - /3 width=5 by and3_intro, fsle_lifts_SO/ - ] - | * #I0 #K0 #V1 #HV1 #HV1X #H0 destruct - elim (lfxs_inv_lref_bind_sn … HY) -HY #I2 #K2 #HK02 #H destruct - lapply (lfxs_fwd_length … HK02) #HK - elim (IH … HK02) [|*: /2 width=4 by fqu_fqup/ ] -IH -HV1 -HK02 - /3 width=5 by fsle_lifts_SO, and3_intro/ - ] - ] -| #l #HG #HL #HT #X #HX #Y #HY destruct -IH - lapply (lfxs_fwd_length … HY) -HY #H0 - >(cpx_inv_gref1 … HX) -X - /3 width=1 by fsle_gref_length, and3_intro/ -| #p #I #V0 #T0 #HG #HL #HT #X #HX #Y #HY destruct - lapply (lfxs_fwd_length … HY) #H0 - elim (lfxs_inv_bind … V0 ? HY) -HY // #HV0 #HT0 - elim (cpx_inv_bind1 … HX) -HX * - [ #V1 #T1 #HV01 #HT01 #H destruct - elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V - elim (IH … HT01 … HT0) -HT01 -HT0 -IH // #H1T #H2T #H3T - /4 width=3 by fsle_bind_eq, fsle_fwd_pair_sn, and3_intro/ - | #T #HT #HXT #H1 #H2 destruct - elim (IH G0 … V0… V0 … HV0) -HV0 // #H1V #H2V #H3V - elim (IH … HT … HT0) -HT -HT0 -IH // #H1T #H2T #H3T - /3 width=5 by fsle_bind, fsle_inv_lifts_sn, and3_intro/ - ] -| #I #V0 #X0 #HG #HL #HT #X #HX #Y #HY destruct - elim (lfxs_inv_flat … HY) -HY #HV0 #HX0 - elim (cpx_inv_flat1 … HX) -HX * - [ #V1 #T1 #HV01 #HT01 #H destruct - elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V - elim (IH … HT01 … HX0) -HT01 -HX0 -IH // #H1T #H2T #H3T - /3 width=3 by fsle_flat, and3_intro/ - | #HX #H destruct - elim (IH G0 … V0… V0 … HV0) -HV0 // #H1V #H2V #H3V - elim (IH … HX … HX0) -HX -HX0 -IH // #H1T #H2T #H3T - /4 width=3 by fsle_flat_sn, fsle_flat_dx_dx, fsle_flat_dx_sn, and3_intro/ - | #HX #H destruct - elim (IH … HX … HV0) -HX -HV0 // #H1V #H2V #H3V - elim (IH G0 … X0… X0 … HX0) -HX0 -IH // #H1T #H2T #H3T - /4 width=3 by fsle_flat_sn, fsle_flat_dx_dx, fsle_flat_dx_sn, and3_intro/ - | #p #V1 #W0 #W1 #T0 #T1 #HV01 #HW01 #HT01 #H1 #H2 #H3 destruct - elim (lfxs_inv_bind … W0 ? HX0) -HX0 // #HW0 #HT0 - elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V - elim (IH … HW01 … HW0) -HW01 -HW0 // #H1W #H2W #H3W - elim (IH … HT01 … HT0) -HT01 -HT0 -IH // #H1T #H2T #H3T - lapply (fsle_fwd_pair_sn … H2T) -H2T #H2T - lapply (fsle_fwd_pair_sn … H3T) -H3T #H3T - @and3_intro [ /3 width=5 by fsle_flat, fsle_bind/ ] (**) (* full auto too slow *) - @fsle_bind_sn_ge /4 width=1 by fsle_shift, fsle_flat_sn, fsle_flat_dx_dx, fsle_flat_dx_sn, fsle_bind_dx_sn/ - | #p #V1 #X1 #W0 #W1 #T0 #T1 #HV01 #HVX1 #HW01 #HT01 #H1 #H2 #H3 destruct - elim (lfxs_inv_bind … W0 ? HX0) -HX0 // #HW0 #HT0 - elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V - elim (IH … HW01 … HW0) -HW01 -HW0 // #H1W #H2W #H3W - elim (IH … HT01 … HT0) -HT01 -HT0 -IH // #H1T #H2T #H3T - lapply (fsle_fwd_pair_sn … H2T) -H2T #H2T - lapply (fsle_fwd_pair_sn … H3T) -H3T #H3T - @and3_intro[ /3 width=5 by fsle_flat, fsle_bind/ ] (**) (* full auto too slow *) - @fsle_bind_sn_ge // - [1,3: /3 width=1 by fsle_flat_dx_dx, fsle_bind_dx_sn/ - |2,4: /4 width=3 by fsle_flat_sn, fsle_flat_dx_sn, fsle_flat_dx_dx, fsle_shift, fsle_lifts_sn/ - ] - ] -] -*) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_fsle.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_fsle.ma index 71f1c41d4..58fcbf307 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_fsle.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_fsle.ma @@ -24,7 +24,6 @@ include "basic_2/rt_transition/lfpx_fqup.ma". (* Note: "⦃L2, T1⦄ ⊆ ⦃L2, T0⦄" does not hold *) (* Note: Take L0 = K0.ⓓ(ⓝW.V), L2 = K0.ⓓW, T0 = #0, T1 = ⬆*[1]V *) (* Note: This invalidates lfpxs_cpx_conf: "∀h,G. s_r_confluent1 … (cpx h G) (lfpxs h G)" *) -(* Note: "⦃L2, T1⦄ ⊆ ⦃L0, T1⦄" may not hold *) (* Basic_2A1: uses: lpx_cpx_frees_trans *) lemma lfpx_cpx_conf_fsge: ∀h,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 → ∀L2. ⦃G, L0⦄ ⊢⬈[h, T0] L2 → ⦃L2, T1⦄ ⊆ ⦃L0, T0⦄. @@ -132,3 +131,7 @@ lemma cpx_lfxs_conf: ∀R,h,G. s_r_confluent1 … (cpx h G) (lfxs R). lemma lfpx_cpx_conf: ∀h,G. s_r_confluent1 … (cpx h G) (lfpx h G). /2 width=5 by cpx_lfxs_conf/ qed-. + +lemma lfpx_cpx_conf_fsge_dx: ∀h,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 → + ∀L2. ⦃G, L0⦄ ⊢⬈[h, T0] L2 → ⦃L2, T1⦄ ⊆ ⦃L0, T1⦄. +/3 width=5 by lfpx_cpx_conf, lfpx_fsge_comp/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma index 9468fe1c7..ea09b60a7 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/static/fsle_fsle.ma @@ -74,6 +74,19 @@ lapply (sle_eq_repl_back2 … Hg … Hgf0) -g0 /4 width=10 by sle_tls, sle_trans, ex4_4_intro/ qed-. +theorem fsle_trans_rc: ∀L1,L,T1,T. |L1| = |L| → ⦃L1, T1⦄ ⊆ ⦃L, T⦄ → + ∀L2,T2. |L| = |L2| → ⦃L, T⦄ ⊆ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄. +#L1 #L #T1 #T #HL1 +* #m1 #m0 #g1 #g0 #Hg1 #Hg0 #Hm #Hg +#L2 #T2 #HL2 +* #n0 #n2 #f0 #f2 #Hf0 #Hf2 #Hn #Hf +lapply (frees_mono … Hg0 … Hf0) -Hg0 -Hf0 #Hgf0 +elim (lveq_inj_length … Hm) // -Hm #H1 #H2 destruct +elim (lveq_inj_length … Hn) // -Hn #H1 #H2 destruct +lapply (sle_eq_repl_back2 … Hg … Hgf0) -g0 +/3 width=10 by lveq_length_eq, sle_trans, ex4_4_intro/ +qed-. + theorem fsle_bind_sn_ge: ∀L1,L2. |L2| ≤ |L1| → ∀V1,T1,T. ⦃L1, V1⦄ ⊆ ⦃L2, T⦄ → ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2, T⦄ → ∀p,I. ⦃L1, ⓑ{p,I}V1.T1⦄ ⊆ ⦃L2, T⦄. 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 37b94745b..c7a9c21e6 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 @@ -122,7 +122,7 @@ table { class "cyan" [ { "rt-transition" * } { [ { "uncounted parallel rst-transition" * } { - [ [ "for closures" ] "fpbq" + "( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpbq_aaa" * ] + [ [ "for closures" ] "fpbq" + "( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpbq_aaa" + "fpbq_fpb" * ] [ [ "proper for closures" ] "fpb" + "( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lfdeq" + "fpb_ffdeq" * ] } ]