X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpx_etc.ma;h=2dcee12eecb6f4751703d2a512f00c5ffa513ffd;hb=990f97071a9939d47be16b36f6045d3b23f218e0;hp=d83d1f063aa0a57cda504a7cb031e30a8bc7a876;hpb=b0eb62e60a2fd73ba39c7a0df112f04131528602;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_etc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_etc.ma index d83d1f063..2dcee12ee 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_etc.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_etc.ma @@ -12,11 +12,11 @@ (* *) (**************************************************************************) -include "basic_2/static/fle_drops.ma". -include "basic_2/static/fle_fqup.ma". -include "basic_2/static/fle_lsubf.ma". -include "basic_2/static/fle_fle.ma". +include "basic_2/static/fsle_drops.ma". +include "basic_2/static/fsle_fqup.ma". +include "basic_2/static/fsle_fsle.ma". include "basic_2/static/lfxs_length.ma". +include "basic_2/static/lfxs_fsle.ma". include "basic_2/rt_transition/cpx.ma". (* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************) @@ -24,36 +24,58 @@ include "basic_2/rt_transition/cpx.ma". (* Properties with context-sensitive free variables *************************) (* Note: "⦃L2, T1⦄ ⊆ ⦃L0, T1⦄" may not hold *) -axiom cpx_lfxs_conf_fle: ∀R. c_reflexive … R → - ∀h,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 → - ∀L2. L0 ⪤*[R, T0] L2 → - ∧∧ ⦃L2, T0⦄ ⊆ ⦃L0, T0⦄ & ⦃L2, T1⦄ ⊆ ⦃L2, T0⦄ - & ⦃L0, T1⦄ ⊆ ⦃L0, T0⦄. +axiom cpx_lfxs_conf_fsle: ∀R,h. c_reflexive … R → + (∨∨ (∀G. (cpx h G) = R) | R_fsle_compatible R) → + ∀G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 → + ∀L2. L0 ⪤*[R, T0] L2 → + ∧∧ ⦃L2, T0⦄ ⊆ ⦃L0, T0⦄ & ⦃L2, T1⦄ ⊆ ⦃L2, T0⦄ + & ⦃L0, T1⦄ ⊆ ⦃L0, T0⦄. (* -#R #HR #h #G #L0 #T0 @(fqup_wf_ind_eq (Ⓕ) … G L0 T0) -G -L0 -T0 +#R #h #H1R #H2R #G #L0 #T0 @(fqup_wf_ind_eq (Ⓕ) … G L0 T0) -G -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 fle_sort_length, and3_intro/ + /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 - elim (IH … HK02) [4,5: /2 width=2 by fqu_fqup, fqu_lref_O/ ] - - lapply (lfxs_fwd_length … HY) -HY #H0 - /3 width=1 by fle_lref_length, and3_intro/ - | * #I0 #K0 #V0 #V1 #HLK0 #HV01 #HX - - elim (lfxs_inv_lref … HY) -HY // #HV0 #HT0 - + 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 fle_gref_length, and3_intro/ + /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 @@ -61,11 +83,11 @@ axiom cpx_lfxs_conf_fle: ∀R. c_reflexive … R → [ #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 fle_bind_eq, fle_fwd_pair_sn, and3_intro/ + /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 fle_bind, fle_inv_lifts_sn, and3_intro/ + /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 @@ -73,36 +95,36 @@ axiom cpx_lfxs_conf_fle: ∀R. c_reflexive … R → [ #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 fle_flat, and3_intro/ + /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 fle_flat_sn, fle_flat_dx_dx, fle_flat_dx_sn, and3_intro/ + /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 fle_flat_sn, fle_flat_dx_dx, fle_flat_dx_sn, and3_intro/ + /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 (fle_fwd_pair_sn … H2T) -H2T #H2T - lapply (fle_fwd_pair_sn … H3T) -H3T #H3T - @and3_intro [ /3 width=5 by fle_flat, fle_bind/ ] (**) (* full auto too slow *) - @fle_bind_sn_ge /4 width=1 by fle_shift, fle_flat_sn, fle_flat_dx_dx, fle_flat_dx_sn, fle_bind_dx_sn/ + 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 (fle_fwd_pair_sn … H2T) -H2T #H2T - lapply (fle_fwd_pair_sn … H3T) -H3T #H3T - @and3_intro[ /3 width=5 by fle_flat, fle_bind/ ] (**) (* full auto too slow *) - @fle_bind_sn_ge // - [1,3: /3 width=1 by fle_flat_dx_dx, fle_bind_dx_sn/ - |2,4: /4 width=3 by fle_flat_sn, fle_flat_dx_sn, fle_flat_dx_dx, fle_shift, fle_lifts_sn/ + 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/ ] ] ] -*) \ No newline at end of file +*)