include "ground_2/lib/arith_2b.ma".
include "basic_2/rt_transition/lpr_lpr.ma".
include "basic_2/rt_computation/cpms_lsubr.ma".
-include "basic_2/rt_computation/cpms_fpbg.ma".
include "basic_2/rt_computation/cpms_cpms.ma".
include "basic_2/dynamic/cnv_drops.ma".
-include "basic_2/dynamic/cnv_preserve_far.ma".
+include "basic_2/dynamic/cnv_preserve_sub.ma".
(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
-(* Far diamond propery with t-bound rt-transition for terms *****************)
+(* Sub diamond propery with t-bound rt-transition for terms *****************)
fact cnv_cpm_conf_lpr_atom_atom_aux (h) (G) (L1) (L2) (I):
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93ª{I} â\9e¡*[0,h] T & â¦\83G, L2â¦\84 â\8a¢ â\93ª{I} ➡*[O,h] T.
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93ª[I] â\9e¡*[0,h] T & â\9dªG,L2â\9d« â\8a¢ â\93ª[I] ➡*[O,h] T.
/2 width=3 by ex2_intro/ qed-.
fact cnv_cpm_conf_lpr_atom_ess_aux (h) (G) (L1) (L2) (s):
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\8b\86s â\9e¡*[1,h] T & â¦\83G,L2â¦\84 â\8a¢ â\8b\86(next h s) ➡*[h] T.
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\8b\86s â\9e¡*[1,h] T & â\9dªG,L2â\9d« â\8a¢ â\8b\86(⫯[h]s) ➡*[h] T.
/3 width=3 by cpm_cpms, ex2_intro/ qed-.
-fact cnv_cpm_conf_lpr_atom_delta_aux (a) (h) (o) (G) (L) (i):
- (â\88\80G0,L0,T0. â¦\83G,L,#iâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84â\8a¢#i![a,h] →
- â\88\80K,V. â¬\87*[i]L ≘ K.ⓓV →
- â\88\80n,XV. â¦\83G,Kâ¦\84 ⊢ V ➡[n,h] XV →
- â\88\80X. â¬\86*[↑i]XV ≘ X →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ #i â\9e¡*[n,h] T & â¦\83G,L2â¦\84 ⊢ X ➡*[h] T.
-#a #h #o #G #L #i #IH #HT #K #V #HLK #n #XV #HVX #X #HXV #L1 #HL1 #L2 #HL2
-lapply (cnv_lref_fwd_drops … HT … HLK) -HT #HV
+fact cnv_cpm_conf_lpr_atom_delta_aux (h) (a) (G) (L) (i):
+ (â\88\80G0,L0,T0. â\9dªG,L,#iâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d«â\8a¢#i![h,a] →
+ â\88\80K,V. â\87©*[i]L ≘ K.ⓓV →
+ â\88\80n,XV. â\9dªG,Kâ\9d« ⊢ V ➡[n,h] XV →
+ â\88\80X. â\87§*[↑i]XV ≘ X →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ #i â\9e¡*[n,h] T & â\9dªG,L2â\9d« ⊢ X ➡*[h] T.
+#h #a #G #L #i #IH #HT #K #V #HLK #n #XV #HVX #X #HXV #L1 #HL1 #L2 #HL2
+lapply (cnv_inv_lref_pair … HT … HLK) -HT #HV
elim (lpr_drops_conf … HLK … HL1) -HL1 // #Y1 #H1 #HLK1
elim (lpr_inv_pair_sn … H1) -H1 #K1 #V1 #HK1 #HV1 #H destruct
elim (lpr_drops_conf … HLK … HL2) -HL2 // #Y2 #H2 #HLK2
elim (lpr_inv_pair_sn … H2) -H2 #K2 #V2 #HK2 #_ #H destruct
lapply (drops_isuni_fwd_drop2 … HLK2) -V2 // #HLK2
lapply (fqup_lref (Ⓣ) … G … HLK) -HLK #HLK
-elim (cnv_cpm_conf_lpr_far … IH … HV1 … HVX … HK1 … HK2) [|*: /2 width=1 by fqup_fpbg/ ] -L -K -V
+elim (cnv_cpm_conf_lpr_sub … IH … HV1 … HVX … HK1 … HK2) [|*: /2 width=1 by fqup_fpbg/ ] -L -K -V
<minus_O_n <minus_n_O #V #HV1 #HVX
elim (cpms_lifts_sn … HVX … HLK2 … HXV) -XV -HLK2 #XV #HVX #HXV
/3 width=6 by cpms_delta_drops, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_atom_ell_aux (a) (h) (o) (G) (L) (i):
- (â\88\80G0,L0,T0. â¦\83G,L,#iâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84â\8a¢#i![a,h] →
- â\88\80K,W. â¬\87*[i]L ≘ K.ⓛW →
- â\88\80n,XW. â¦\83G,Kâ¦\84 ⊢ W ➡[n,h] XW →
- â\88\80X. â¬\86*[↑i]XW ≘ X →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ #i â\9e¡*[â\86\91n,h] T & â¦\83G,L2â¦\84 ⊢ X ➡*[h] T.
-#a #h #o #G #L #i #IH #HT #K #W #HLK #n #XW #HWX #X #HXW #L1 #HL1 #L2 #HL2
-lapply (cnv_lref_fwd_drops … HT … HLK) -HT #HW
+fact cnv_cpm_conf_lpr_atom_ell_aux (h) (a) (G) (L) (i):
+ (â\88\80G0,L0,T0. â\9dªG,L,#iâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d«â\8a¢#i![h,a] →
+ â\88\80K,W. â\87©*[i]L ≘ K.ⓛW →
+ â\88\80n,XW. â\9dªG,Kâ\9d« ⊢ W ➡[n,h] XW →
+ â\88\80X. â\87§*[↑i]XW ≘ X →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ #i â\9e¡*[â\86\91n,h] T & â\9dªG,L2â\9d« ⊢ X ➡*[h] T.
+#h #a #G #L #i #IH #HT #K #W #HLK #n #XW #HWX #X #HXW #L1 #HL1 #L2 #HL2
+lapply (cnv_inv_lref_pair … HT … HLK) -HT #HW
elim (lpr_drops_conf … HLK … HL1) -HL1 // #Y1 #H1 #HLK1
elim (lpr_inv_pair_sn … H1) -H1 #K1 #W1 #HK1 #HW1 #H destruct
elim (lpr_drops_conf … HLK … HL2) -HL2 // #Y2 #H2 #HLK2
elim (lpr_inv_pair_sn … H2) -H2 #K2 #W2 #HK2 #_ #H destruct
lapply (drops_isuni_fwd_drop2 … HLK2) -W2 // #HLK2
lapply (fqup_lref (Ⓣ) … G … HLK) -HLK #HLK
-elim (cnv_cpm_conf_lpr_far … IH … HW1 … HWX … HK1 … HK2) [|*: /2 width=1 by fqup_fpbg/ ] -L -K -W
+elim (cnv_cpm_conf_lpr_sub … IH … HW1 … HWX … HK1 … HK2) [|*: /2 width=1 by fqup_fpbg/ ] -L -K -W
<minus_O_n <minus_n_O #W #HW1 #HWX
elim (cpms_lifts_sn … HWX … HLK2 … HXW) -XW -HLK2 #XW #HWX #HXW
/3 width=6 by cpms_ell_drops, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_delta_delta_aux (a) (h) (o) (I) (G) (L) (i):
- (â\88\80G0,L0,T0. â¦\83G,L,#iâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84â\8a¢#i![a,h] →
- â\88\80K1,V1. â¬\87*[i]L â\89\98 K1.â\93\91{I}V1 â\86\92 â\88\80K2,V2. â¬\87*[i]L â\89\98 K2.â\93\91{I}V2 →
- â\88\80n1,XV1. â¦\83G,K1â¦\84 â\8a¢ V1 â\9e¡[n1,h] XV1 â\86\92 â\88\80n2,XV2. â¦\83G,K2â¦\84 ⊢ V2 ➡[n2,h] XV2 →
- â\88\80X1. â¬\86*[â\86\91i]XV1 â\89\98 X1 â\86\92 â\88\80X2. â¬\86*[↑i]XV2 ≘ X2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ X1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ X2 ➡*[n1-n2,h] T.
-#a #h #o #I #G #L #i #IH #HT
+fact cnv_cpm_conf_lpr_delta_delta_aux (h) (a) (I) (G) (L) (i):
+ (â\88\80G0,L0,T0. â\9dªG,L,#iâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d«â\8a¢#i![h,a] →
+ â\88\80K1,V1. â\87©*[i]L â\89\98 K1.â\93\91[I]V1 â\86\92 â\88\80K2,V2. â\87©*[i]L â\89\98 K2.â\93\91[I]V2 →
+ â\88\80n1,XV1. â\9dªG,K1â\9d« â\8a¢ V1 â\9e¡[n1,h] XV1 â\86\92 â\88\80n2,XV2. â\9dªG,K2â\9d« ⊢ V2 ➡[n2,h] XV2 →
+ â\88\80X1. â\87§*[â\86\91i]XV1 â\89\98 X1 â\86\92 â\88\80X2. â\87§*[↑i]XV2 ≘ X2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ X1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« ⊢ X2 ➡*[n1-n2,h] T.
+#h #a #I #G #L #i #IH #HT
#K #V #HLK #Y #X #HLY #n1 #XV1 #HVX1 #n2 #XV2 #HVX2 #X1 #HXV1 #X2 #HXV2
#L1 #HL1 #L2 #HL2
lapply (drops_mono … HLY … HLK) -HLY #H destruct
-lapply (cnv_lref_fwd_drops … HT … HLK) -HT #HV
+lapply (cnv_inv_lref_pair … HT … HLK) -HT #HV
elim (lpr_drops_conf … HLK … HL1) -HL1 // #Y1 #H1 #HLK1
elim (lpr_inv_pair_sn … H1) -H1 #K1 #V1 #HK1 #_ #H destruct
lapply (drops_isuni_fwd_drop2 … HLK1) -V1 // #HLK1
elim (lpr_inv_pair_sn … H2) -H2 #K2 #V2 #HK2 #_ #H destruct
lapply (drops_isuni_fwd_drop2 … HLK2) -V2 // #HLK2
lapply (fqup_lref (Ⓣ) … G … HLK) -HLK #HLK
-elim (cnv_cpm_conf_lpr_far … IH … HVX1 … HVX2 … HK1 … HK2) [|*: /2 width=1 by fqup_fpbg/ ] -L -K -V
+elim (cnv_cpm_conf_lpr_sub … IH … HVX1 … HVX2 … HK1 … HK2) [|*: /2 width=1 by fqup_fpbg/ ] -L -K -V
#V #HVX1 #HVX2
elim (cpms_lifts_sn … HVX1 … HLK1 … HXV1) -XV1 -HLK1 #W1 #HVW1 #HXW1
/3 width=11 by cpms_lifts_bi, ex2_intro/
qed-.
fact cnv_cpm_conf_lpr_delta_ell_aux (L) (K1) (K2) (V) (W) (i):
- â¬\87*[i]L â\89\98 K1.â\93\93V â\86\92 â¬\87*[i]L ≘ K2.ⓛW → ⊥.
+ â\87©*[i]L â\89\98 K1.â\93\93V â\86\92 â\87©*[i]L ≘ K2.ⓛW → ⊥.
#L #K1 #K2 #V #W #i #HLK1 #HLK2
lapply (drops_mono … HLK2 … HLK1) -L -i #H destruct
qed-.
-fact cnv_cpm_conf_lpr_bind_bind_aux (a) (h) (o) (p) (I) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\91{p,I}V.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V.T ![a,h] →
- â\88\80V1. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â¦\83G,Lâ¦\84 ⊢ V ➡[h] V2 →
- â\88\80n1,T1. â¦\83G,L.â\93\91{I}Vâ¦\84 â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,L.â\93\91{I}Vâ¦\84 ⊢ T ➡[n2,h] T2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93\91{p,I}V1.T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 â\8a¢ â\93\91{p,I}V2.T2 ➡*[n1-n2,h] T.
-#a #h #o #p #I #G0 #L0 #V0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_bind_bind_aux (h) (a) (p) (I) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\91[p,I]V.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V.T ![h,a] →
+ â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h] V2 →
+ â\88\80n1,T1. â\9dªG,L.â\93\91[I]Vâ\9d« â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\91[I]Vâ\9d« ⊢ T ➡[n2,h] T2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\91[p,I]V1.T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« â\8a¢ â\93\91[p,I]V2.T2 ➡*[n1-n2,h] T.
+#h #a #p #I #G0 #L0 #V0 #T0 #IH #H0
#V1 #HV01 #V2 #HV02 #n1 #T1 #HT01 #n2 #T2 #HT02
#L1 #HL01 #L2 #HL02
elim (cnv_inv_bind … H0) -H0 #HV0 #HT0
elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2
-elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓑ{I}V1) … (L2.ⓑ{I}V2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 (L1.ⓑ[I]V1) … (L2.ⓑ[I]V2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
#T #HT1 #HT2 -L0 -V0 -T0
/3 width=5 by cpms_bind_dx, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_bind_zeta_aux (a) (h) (o) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,+â\93\93V.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ +â\93\93V.T ![a,h] →
- â\88\80V1. â¦\83G,Lâ¦\84 â\8a¢V â\9e¡[h] V1 â\86\92 â\88\80n1,T1. â¦\83G,L.â\93\93Vâ¦\84 â\8a¢ T â\9e¡[n1,h] T1 â\86\92
- â\88\80T2. â¬\86*[1]T2 â\89\98 T â\86\92 â\88\80n2,XT2. â¦\83G,Lâ¦\84 ⊢ T2 ➡[n2,h] XT2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ +â\93\93V1.T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ XT2 ➡*[n1-n2,h] T.
-#a #h #o #G0 #L0 #V0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_bind_zeta_aux (h) (a) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,+â\93\93V.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ +â\93\93V.T ![h,a] →
+ â\88\80V1. â\9dªG,Lâ\9d« â\8a¢V â\9e¡[h] V1 â\86\92 â\88\80n1,T1. â\9dªG,L.â\93\93Vâ\9d« â\8a¢ T â\9e¡[n1,h] T1 â\86\92
+ â\88\80T2. â\87§*[1]T2 â\89\98 T â\86\92 â\88\80n2,XT2. â\9dªG,Lâ\9d« ⊢ T2 ➡[n2,h] XT2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ +â\93\93V1.T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« ⊢ XT2 ➡*[n1-n2,h] T.
+#h #a #G0 #L0 #V0 #T0 #IH #H0
#V1 #HV01 #n1 #T1 #HT01 #T2 #HT20 #n2 #XT2 #HXT2
#L1 #HL01 #L2 #HL02
elim (cnv_inv_bind … H0) -H0 #_ #HT0
lapply (cnv_inv_lifts … HT0 (Ⓣ) … L0 … HT20) -HT0
-[ /3 width=3 by drops_refl, drops_drop/ ] #HT2
+[ /3 width=3 by drops_refl, drops_drop/ ] #HT2
elim (cpm_inv_lifts_sn … HT01 (Ⓣ) … L0 … HT20) -HT01
[| /3 width=1 by drops_refl, drops_drop/ ] #XT1 #HXT1 #HXT12
-elim (cnv_cpm_conf_lpr_far … IH … HXT12 … HXT2 … HL01 … HL02)
+elim (cnv_cpm_conf_lpr_sub … IH … HXT12 … HXT2 … HL01 … HL02)
[|*: /3 width=1 by fqup_fpbg, fqup_zeta/ ] -L0 -T0 -V0 #T #HT1 #HT2
/3 width=3 by cpms_zeta, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_zeta_zeta_aux (a) (h) (o) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,+â\93\93V.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ +â\93\93V.T ![a,h] →
- â\88\80T1. â¬\86*[1]T1 â\89\98 T â\86\92 â\88\80T2. â¬\86*[1]T2 ≘ T →
- â\88\80n1,XT1. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡[n1,h] XT1 â\86\92 â\88\80n2,XT2. â¦\83G,Lâ¦\84 ⊢ T2 ➡[n2,h] XT2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ XT1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ XT2 ➡*[n1-n2,h] T.
-#a #h #o #G0 #L0 #V0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_zeta_zeta_aux (h) (a) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,+â\93\93V.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ +â\93\93V.T ![h,a] →
+ â\88\80T1. â\87§*[1]T1 â\89\98 T â\86\92 â\88\80T2. â\87§*[1]T2 ≘ T →
+ â\88\80n1,XT1. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[n1,h] XT1 â\86\92 â\88\80n2,XT2. â\9dªG,Lâ\9d« ⊢ T2 ➡[n2,h] XT2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ XT1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« ⊢ XT2 ➡*[n1-n2,h] T.
+#h #a #G0 #L0 #V0 #T0 #IH #H0
#T1 #HT10 #T2 #HT20 #n1 #XT1 #HXT1 #n2 #XT2 #HXT2
#L1 #HL01 #L2 #HL02
elim (cnv_inv_bind … H0) -H0 #_ #HT0
lapply (lifts_inj … HT10 … HT20) -HT10 #H destruct
lapply (cnv_inv_lifts … HT0 (Ⓣ) … L0 … HT20) -HT0
[ /3 width=3 by drops_refl, drops_drop/ ] #HT2
-elim (cnv_cpm_conf_lpr_far … IH … HXT1 … HXT2 … HL01 … HL02)
+elim (cnv_cpm_conf_lpr_sub … IH … HXT1 … HXT2 … HL01 … HL02)
[|*: /3 width=1 by fqup_fpbg, fqup_zeta/ ] -L0 -T0 #T #HT1 #HT2
/2 width=3 by ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_appl_appl_aux (a) (h) (o) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\90V.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.T ![a,h] →
- â\88\80V1. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â¦\83G,Lâ¦\84 ⊢ V ➡[h] V2 →
- â\88\80n1,T1. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,Lâ¦\84 ⊢ T ➡[n2,h] T2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93\90V1.T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ ⓐV2.T2 ➡*[n1-n2,h] T.
-#a #h #o #G0 #L0 #V0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_appl_appl_aux (h) (a) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\90V.T ![h,a] →
+ â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h] V2 →
+ â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T ➡[n2,h] T2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\90V1.T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« ⊢ ⓐV2.T2 ➡*[n1-n2,h] T.
+#h #a #G0 #L0 #V0 #T0 #IH #H0
#V1 #HV01 #V2 #HV02 #n1 #T1 #HT01 #n2 #T2 #HT02
#L1 #HL01 #L2 #HL02
elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #HT0 #_ #_ -n0 -p0 -X01 -X02
elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2
-elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
#T #HT1 #HT2 -L0 -V0 -T0
/3 width=5 by cpms_appl_dx, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_appl_beta_aux (a) (h) (o) (p) (G) (L) (V) (W) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\90V.â\93\9b{p}W.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.â\93\9b{p}W.T ![a,h] →
- â\88\80V1. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â¦\83G,Lâ¦\84 ⊢ V ➡[h] V2 →
- â\88\80W2. â¦\83G,Lâ¦\84 ⊢ W ➡[h] W2 →
- â\88\80n1,T1. â¦\83G,Lâ¦\84 â\8a¢ â\93\9b{p}W.T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,L.â\93\9bWâ¦\84 ⊢ T ➡[n2,h] T2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93\90V1.T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 â\8a¢ â\93\93{p}ⓝW2.V2.T2 ➡*[n1-n2,h] T.
-#a #h #o #p #G0 #L0 #V0 #W0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_appl_beta_aux (h) (a) (p) (G) (L) (V) (W) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.â\93\9b[p]W.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\90V.â\93\9b[p]W.T ![h,a] →
+ â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h] V2 →
+ â\88\80W2. â\9dªG,Lâ\9d« ⊢ W ➡[h] W2 →
+ â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ â\93\9b[p]W.T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\9bWâ\9d« ⊢ T ➡[n2,h] T2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\90V1.T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« â\8a¢ â\93\93[p]ⓝW2.V2.T2 ➡*[n1-n2,h] T.
+#h #a #p #G0 #L0 #V0 #W0 #T0 #IH #H0
#V1 #HV01 #V2 #HV02 #W2 #HW02 #n1 #X #HX #n2 #T2 #HT02
#L1 #HL01 #L2 #HL02
elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #H0 #_ #_ -n0 -p0 -X01 -X02
elim (cpm_inv_abst1 … HX) -HX #W1 #T1 #HW01 #HT01 #H destruct
elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2
elim (cpr_conf_lpr … HW01 … HW02 … HL01 … HL02) #W #HW1 #HW2
-elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
#T #HT1 #HT2 -L0 -V0 -W0 -T0
lapply (lsubr_cpms_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 [ /2 width=1 by lsubr_beta/ ] #HT2
/4 width=5 by cpms_beta_dx, cpms_bind_dx, cpm_cast, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_appl_theta_aux (a) (h) (o) (p) (G) (L) (V) (W) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\90V.â\93\93{p}W.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.â\93\93{p}W.T ![a,h] →
- â\88\80V1. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â¦\83G,Lâ¦\84 ⊢ V ➡[h] V2 →
- â\88\80W2. â¦\83G,Lâ¦\84 ⊢ W ➡[h] W2 →
- â\88\80n1,T1. â¦\83G,Lâ¦\84 â\8a¢ â\93\93{p}W.T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,L.â\93\93Wâ¦\84 ⊢ T ➡[n2,h] T2 →
- â\88\80U2. â¬\86*[1]V2 ≘ U2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93\90V1.T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 â\8a¢ â\93\93{p}W2.ⓐU2.T2 ➡*[n1-n2,h] T.
-#a #h #o #p #G0 #L0 #V0 #W0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_appl_theta_aux (h) (a) (p) (G) (L) (V) (W) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.â\93\93[p]W.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\90V.â\93\93[p]W.T ![h,a] →
+ â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h] V2 →
+ â\88\80W2. â\9dªG,Lâ\9d« ⊢ W ➡[h] W2 →
+ â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ â\93\93[p]W.T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\93Wâ\9d« ⊢ T ➡[n2,h] T2 →
+ â\88\80U2. â\87§*[1]V2 ≘ U2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\90V1.T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« â\8a¢ â\93\93[p]W2.ⓐU2.T2 ➡*[n1-n2,h] T.
+#h #a #p #G0 #L0 #V0 #W0 #T0 #IH #H0
#V1 #HV01 #V2 #HV02 #W2 #HW02 #n1 #X #HX #n2 #T2 #HT02 #U2 #HVU2
#L1 #HL01 #L2 #HL02
elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #H0 #_ #_ -n0 -p0 -X01 -X02
elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2
elim (cpm_inv_abbr1 … HX) -HX *
[ #W1 #T1 #HW01 #HT01 #H destruct
- elim (cpm_lifts_sn … HV2 (Ⓣ) … (L2.ⓓW2) … HVU2) -HVU2 [| /3 width=1 by drops_refl, drops_drop/ ] #U #HVU #HU2
+ elim (cpm_lifts_sn … HV2 (Ⓣ) … (L2.ⓓW2) … HVU2) -HV2 -HVU2 [| /3 width=1 by drops_refl, drops_drop/ ] #U #HVU #HU2
elim (cpr_conf_lpr … HW01 … HW02 … HL01 … HL02) #W #HW1 #HW2
- elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓓW1) … (L2.ⓓW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
+ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 (L1.ⓓW1) … (L2.ⓓW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
#T #HT1 #HT2 -L0 -V0 -W0 -T0
/4 width=7 by cpms_theta_dx, cpms_appl_dx, cpms_bind_dx, ex2_intro/
| #X0 #HXT0 #H1X0 #H destruct
- lapply (cnv_inv_lifts … HT0 (Ⓣ) … L0 … HXT0) -HT0 [ /3 width=3 by drops_refl, drops_drop/ ] #H2X0
+ lapply (cnv_inv_lifts … HT0 (Ⓣ) … L0 … HXT0) -HT0 [ /3 width=3 by drops_refl, drops_drop/ ] #H2X0
elim (cpm_inv_lifts_sn … HT02 (Ⓣ) … L0 … HXT0) -HT02 [| /3 width=1 by drops_refl, drops_drop/ ] #X2 #HXT2 #HX02
- elim (cnv_cpm_conf_lpr_far … IH … H1X0 … HX02 … HL01 … HL02)
+ elim (cnv_cpm_conf_lpr_sub … IH … H1X0 … HX02 … HL01 … HL02)
[|*: /4 width=5 by fqup_fpbg, fqup_strap1, fqu_drop/ ] #T #HT1 #HT2 -L0 -V0 -W0 -T0
/4 width=8 by cpms_zeta, cpms_appl_dx, lifts_flat, ex2_intro/
]
qed-.
-fact cnv_cpm_conf_lpr_beta_beta_aux (a) (h) (o) (p) (G) (L) (V) (W) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\90V.â\93\9b{p}W.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.â\93\9b{p}W.T ![a,h] →
- â\88\80V1. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â¦\83G,Lâ¦\84 ⊢ V ➡[h] V2 →
- â\88\80W1. â¦\83G,Lâ¦\84 â\8a¢ W â\9e¡[h] W1 â\86\92 â\88\80W2. â¦\83G,Lâ¦\84 ⊢ W ➡[h] W2 →
- â\88\80n1,T1. â¦\83G,L.â\93\9bWâ¦\84 â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,L.â\93\9bWâ¦\84 ⊢ T ➡[n2,h] T2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93\93{p}â\93\9dW1.V1.T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 â\8a¢ â\93\93{p}ⓝW2.V2.T2 ➡*[n1-n2,h] T.
-#a #h #o #p #G0 #L0 #V0 #W0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_beta_beta_aux (h) (a) (p) (G) (L) (V) (W) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.â\93\9b[p]W.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\90V.â\93\9b[p]W.T ![h,a] →
+ â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h] V2 →
+ â\88\80W1. â\9dªG,Lâ\9d« â\8a¢ W â\9e¡[h] W1 â\86\92 â\88\80W2. â\9dªG,Lâ\9d« ⊢ W ➡[h] W2 →
+ â\88\80n1,T1. â\9dªG,L.â\93\9bWâ\9d« â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\9bWâ\9d« ⊢ T ➡[n2,h] T2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\93[p]â\93\9dW1.V1.T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« â\8a¢ â\93\93[p]ⓝW2.V2.T2 ➡*[n1-n2,h] T.
+#h #a #p #G0 #L0 #V0 #W0 #T0 #IH #H0
#V1 #HV01 #V2 #HV02 #W1 #HW01 #W2 #HW02 #n1 #T1 #HT01 #n2 #T2 #HT02
#L1 #HL01 #L2 #HL02
elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #H0 #_ #_ -n0 -p0 -X01 -X02
elim (cnv_inv_bind … H0) -H0 #HW0 #HT0
elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2
elim (cpr_conf_lpr … HW01 … HW02 … HL01 … HL02) #W #HW1 #HW2
-elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
#T #HT1 #HT2 -L0 -V0 -W0 -T0
lapply (lsubr_cpms_trans … HT1 (L1.ⓓⓝW1.V1) ?) -HT1 /2 width=1 by lsubr_beta/ #HT1
lapply (lsubr_cpms_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1 by lsubr_beta/ #HT2
/4 width=5 by cpms_bind_dx, cpm_eps, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_theta_theta_aux (a) (h) (o) (p) (G) (L) (V) (W) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\90V.â\93\93{p}W.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.â\93\93{p}W.T ![a,h] →
- â\88\80V1. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â¦\83G,Lâ¦\84 ⊢ V ➡[h] V2 →
- â\88\80W1. â¦\83G,Lâ¦\84 â\8a¢ W â\9e¡[h] W1 â\86\92 â\88\80W2. â¦\83G,Lâ¦\84 ⊢ W ➡[h] W2 →
- â\88\80n1,T1. â¦\83G,L.â\93\93Wâ¦\84 â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,L.â\93\93Wâ¦\84 ⊢ T ➡[n2,h] T2 →
- â\88\80U1. â¬\86*[1]V1 â\89\98 U1 â\86\92 â\88\80U2. â¬\86*[1]V2 ≘ U2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93\93{p}W1.â\93\90U1.T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 â\8a¢ â\93\93{p}W2.ⓐU2.T2 ➡*[n1-n2,h] T.
-#a #h #o #p #G0 #L0 #V0 #W0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_theta_theta_aux (h) (a) (p) (G) (L) (V) (W) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.â\93\93[p]W.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\90V.â\93\93[p]W.T ![h,a] →
+ â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h] V2 →
+ â\88\80W1. â\9dªG,Lâ\9d« â\8a¢ W â\9e¡[h] W1 â\86\92 â\88\80W2. â\9dªG,Lâ\9d« ⊢ W ➡[h] W2 →
+ â\88\80n1,T1. â\9dªG,L.â\93\93Wâ\9d« â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\93Wâ\9d« ⊢ T ➡[n2,h] T2 →
+ â\88\80U1. â\87§*[1]V1 â\89\98 U1 â\86\92 â\88\80U2. â\87§*[1]V2 ≘ U2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\93[p]W1.â\93\90U1.T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« â\8a¢ â\93\93[p]W2.ⓐU2.T2 ➡*[n1-n2,h] T.
+#h #a #p #G0 #L0 #V0 #W0 #T0 #IH #H0
#V1 #HV01 #V2 #HV02 #W1 #HW01 #W2 #HW02 #n1 #T1 #HT01 #n2 #T2 #HT02 #U1 #HVU1 #U2 #HVU2
#L1 #HL01 #L2 #HL02
elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #H0 #_ #_ -n0 -p0 -X01 -X02
elim (cnv_inv_bind … H0) -H0 #HW0 #HT0
elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2
elim (cpr_conf_lpr … HW01 … HW02 … HL01 … HL02) #W #HW1 #HW2
-elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓓW1) … (L2.ⓓW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 (L1.ⓓW1) … (L2.ⓓW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ]
#T #HT1 #HT2 -L0 -V0 -W0 -T0
elim (cpm_lifts_sn … HV1 (Ⓣ) … (L1.ⓓW1) … HVU1) -V1 [| /3 width=1 by drops_refl, drops_drop/ ] #U #HVU #HU1
lapply (cpm_lifts_bi … HV2 (Ⓣ) … (L2.ⓓW2) … HVU2 … HVU) -V2 -V [ /3 width=1 by drops_refl, drops_drop/ ] #HU2
/4 width=7 by cpms_appl_dx, cpms_bind_dx, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_cast_cast_aux (a) (h) (o) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\9dV.T ![a,h] →
- â\88\80n1,V1. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡[n1,h] V1 â\86\92 â\88\80n2,V2. â¦\83G,Lâ¦\84 ⊢ V ➡[n2,h] V2 →
- â\88\80T1. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80T2. â¦\83G,Lâ¦\84 ⊢ T ➡[n2,h] T2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93\9dV1.T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ ⓝV2.T2 ➡*[n1-n2,h] T.
-#a #h #o #G0 #L0 #V0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_cast_cast_aux (h) (a) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[n1,h] V1 â\86\92 â\88\80n2,V2. â\9dªG,Lâ\9d« ⊢ V ➡[n2,h] V2 →
+ â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80T2. â\9dªG,Lâ\9d« ⊢ T ➡[n2,h] T2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\9dV1.T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« ⊢ ⓝV2.T2 ➡*[n1-n2,h] T.
+#h #a #G0 #L0 #V0 #T0 #IH #H0
#n1 #V1 #HV01 #n2 #V2 #HV02 #T1 #HT01 #T2 #HT02
#L1 #HL01 #L2 #HL02
elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #HT0 #_ #_ -X0
-elim (cnv_cpm_conf_lpr_far … IH … HV01 … HV02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
-elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HV01 … HV02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
#T #HT1 #HT2 #V #HV1 #HV2 -L0 -V0 -T0
/3 width=5 by cpms_cast, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_cast_epsilon_aux (a) (h) (o) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\9dV.T ![a,h] →
- â\88\80n1,V1. â¦\83G,Lâ¦\84 ⊢ V ➡[n1,h] V1 →
- â\88\80T1. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,Lâ¦\84 ⊢ T ➡[n2,h] T2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93\9dV1.T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ T2 ➡*[n1-n2,h] T.
-#a #h #o #G0 #L0 #V0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_cast_epsilon_aux (h) (a) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,V1. â\9dªG,Lâ\9d« ⊢ V ➡[n1,h] V1 →
+ â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T ➡[n2,h] T2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\9dV1.T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« ⊢ T2 ➡*[n1-n2,h] T.
+#h #a #G0 #L0 #V0 #T0 #IH #H0
#n1 #V1 #HV01 #T1 #HT01 #n2 #T2 #HT02
#L1 #HL01 #L2 #HL02
elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #HT0 #_ #_ -X0
-elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
#T #HT1 #HT2 -L0 -V0 -T0
/3 width=3 by cpms_eps, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_cast_ee_aux (a) (h) (o) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpm_trans_lpr a h G0 L0 T0) →
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\9dV.T ![a,h] →
- â\88\80n1,V1. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡[n1,h] V1 â\86\92 â\88\80n2,V2. â¦\83G,Lâ¦\84 ⊢ V ➡[n2,h] V2 →
- â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T ➡[n1,h] T1 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ â\93\9dV1.T1 â\9e¡*[â\86\91n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ V2 ➡*[n1-↑n2,h] T.
-#a #h #o #G0 #L0 #V0 #T0 #IH2 #IH1 #H0
+fact cnv_cpm_conf_lpr_cast_ee_aux (h) (a) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[n1,h] V1 â\86\92 â\88\80n2,V2. â\9dªG,Lâ\9d« ⊢ V ➡[n2,h] V2 →
+ â\88\80T1. â\9dªG,Lâ\9d« ⊢ T ➡[n1,h] T1 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\9dV1.T1 â\9e¡*[â\86\91n2-n1,h] T & â\9dªG,L2â\9d« ⊢ V2 ➡*[n1-↑n2,h] T.
+#h #a #G0 #L0 #V0 #T0 #IH2 #IH1 #H0
#n1 #V1 #HV01 #n2 #V2 #HV02 #T1 #HT01
#L1 #HL01 #L2 #HL02 -HV01
elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #HT0 #HVX0 #HTX0
-lapply (cnv_cpms_trans_lpr_far … IH2 … HVX0 … L0 ?) [4:|*: /2 width=1 by fqup_fpbg/ ] #HX0
-elim (cnv_cpms_strip_lpr_far … IH1 … HVX0 … HV02 … L0 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
-elim (cnv_cpms_strip_lpr_far … IH1 … HTX0 … HT01 … L0 … HL01) [|*: /2 width=1 by fqup_fpbg/ ]
+lapply (cnv_cpms_trans_lpr_sub … IH2 … HVX0 … L0 ?) [4:|*: /2 width=1 by fqup_fpbg/ ] #HX0
+elim (cnv_cpms_strip_lpr_sub … IH1 … HVX0 … HV02 … L0 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
+elim (cnv_cpms_strip_lpr_sub … IH1 … HTX0 … HT01 … L0 … HL01) [|*: /2 width=1 by fqup_fpbg/ ]
-HV02 -HTX0 -HT01 <minus_O_n <minus_n_O #T #HT2 #HT1 #V #HV1 #HV2
elim (IH1 … HV1 … HT2 … HL02 … HL01) [|*: /2 width=4 by fqup_cpms_fwd_fpbg/ ]
-L0 -V0 -T0 -X0 #U #HVU #HTU
/3 width=3 by cpms_eps, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_epsilon_epsilon_aux (a) (h) (o) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\9dV.T ![a,h] →
- â\88\80n1,T1. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,Lâ¦\84 ⊢ T ➡[n2,h] T2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ T2 ➡*[n1-n2,h] T.
-#a #h #o #G0 #L0 #V0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_epsilon_epsilon_aux (h) (a) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T ➡[n2,h] T2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« ⊢ T2 ➡*[n1-n2,h] T.
+#h #a #G0 #L0 #V0 #T0 #IH #H0
#n1 #T1 #HT01 #n2 #T2 #HT02
#L1 #HL01 #L2 #HL02
elim (cnv_inv_cast … H0) -H0 #X0 #_ #HT0 #_ #_ -X0
-elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
#T #HT1 #HT2 -L0 -V0 -T0
/2 width=3 by ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_epsilon_ee_aux (a) (h) (o) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpm_trans_lpr a h G0 L0 T0) →
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\9dV.T ![a,h] →
- â\88\80n1,T1. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,V2. â¦\83G,Lâ¦\84 ⊢ V ➡[n2,h] V2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ T1 â\9e¡*[â\86\91n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ V2 ➡*[n1-↑n2,h] T.
-#a #h #o #G0 #L0 #V0 #T0 #IH2 #IH1 #H0
+fact cnv_cpm_conf_lpr_epsilon_ee_aux (h) (a) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[n1,h] T1 â\86\92 â\88\80n2,V2. â\9dªG,Lâ\9d« ⊢ V ➡[n2,h] V2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡*[â\86\91n2-n1,h] T & â\9dªG,L2â\9d« ⊢ V2 ➡*[n1-↑n2,h] T.
+#h #a #G0 #L0 #V0 #T0 #IH2 #IH1 #H0
#n1 #T1 #HT01 #n2 #V2 #HV02
#L1 #HL01 #L2 #HL02
elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #HT0 #HVX0 #HTX0
-lapply (cnv_cpms_trans_lpr_far … IH2 … HVX0 … L0 ?) [4:|*: /2 width=1 by fqup_fpbg/ ] #HX0
-elim (cnv_cpms_strip_lpr_far … IH1 … HVX0 … HV02 … L0 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
-elim (cnv_cpms_strip_lpr_far … IH1 … HTX0 … HT01 … L0 … HL01) [|*: /2 width=1 by fqup_fpbg/ ]
+lapply (cnv_cpms_trans_lpr_sub … IH2 … HVX0 … L0 ?) [4:|*: /2 width=1 by fqup_fpbg/ ] #HX0
+elim (cnv_cpms_strip_lpr_sub … IH1 … HVX0 … HV02 … L0 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
+elim (cnv_cpms_strip_lpr_sub … IH1 … HTX0 … HT01 … L0 … HL01) [|*: /2 width=1 by fqup_fpbg/ ]
-HV02 -HTX0 -HT01 <minus_O_n <minus_n_O #T #HT2 #HT1 #V #HV1 #HV2
elim (IH1 … HV1 … HT2 … HL02 … HL01) [|*: /2 width=4 by fqup_cpms_fwd_fpbg/ ]
-L0 -V0 -T0 -X0 #U #HVU #HTU
/2 width=3 by ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_ee_ee_aux (a) (h) (o) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h,o] â¦\83G0,L0,T0â¦\84 â\86\92 IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
- â¦\83G,Lâ¦\84 â\8a¢ â\93\9dV.T ![a,h] →
- â\88\80n1,V1. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡[n1,h] V1 â\86\92 â\88\80n2,V2. â¦\83G,Lâ¦\84 ⊢ V ➡[n2,h] V2 →
- â\88\80L1. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â¦\83G,Lâ¦\84 ⊢ ➡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ V1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 ⊢ V2 ➡*[n1-n2,h] T.
-#a #h #o #G0 #L0 #V0 #T0 #IH #H0
+fact cnv_cpm_conf_lpr_ee_ee_aux (h) (a) (G) (L) (V) (T):
+ (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« >[h] â\9dªG0,L0,T0â\9d« â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9dªG,Lâ\9d« â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[n1,h] V1 â\86\92 â\88\80n2,V2. â\9dªG,Lâ\9d« ⊢ V ➡[n2,h] V2 →
+ â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h] L2 →
+ â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ V1 â\9e¡*[n2-n1,h] T & â\9dªG,L2â\9d« ⊢ V2 ➡*[n1-n2,h] T.
+#h #a #G0 #L0 #V0 #T0 #IH #H0
#n1 #V1 #HV01 #n2 #V2 #HV02
#L1 #HL01 #L2 #HL02
elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #_ #_ #_ -X0
-elim (cnv_cpm_conf_lpr_far … IH … HV01 … HV02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
+elim (cnv_cpm_conf_lpr_sub … IH … HV01 … HV02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ]
#V #HV1 #HV2 -L0 -V0 -T0
/2 width=3 by ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_aux (a) (h) (o):
- ∀G0,L0,T0.
- (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) →
- (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
- ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpm_conf_lpr a h G1 L1 T1.
-#a #h #o #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
+fact cnv_cpm_conf_lpr_aux (h) (a):
+ ∀G0,L0,T0.
+ (∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
+ (∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
+ ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpm_conf_lpr h a G1 L1 T1.
+#h #a #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
[ #I #HG0 #HL0 #HT0 #HT #n1 #X1 #HX1 #n2 #X2 #HX2 #L1 #HL1 #L2 #HL2 destruct
elim (cpm_inv_atom1_drops … HX1) -HX1 *
elim (cpm_inv_atom1_drops … HX2) -HX2 *
- [ #H21 #H22 #H11 #H12 destruct -L -a -o
+ [ #H21 #H22 #H11 #H12 destruct -a -L
<minus_O_n
/2 width=1 by cnv_cpm_conf_lpr_atom_atom_aux/
- | #s2 #H21 #H22 #H23 #H11 #H12 destruct -L -a -o
+ | #s2 #H21 #H22 #H23 #H11 #H12 destruct -a -L
<minus_O_n <minus_n_O
/2 width=1 by cnv_cpm_conf_lpr_atom_ess_aux/
| #K2 #V2 #XV2 #i #HLK2 #HVX2 #HXV2 #H21 #H11 #H12 destruct -IH2
| #m2 #K2 #W2 #XW2 #i #HLK2 #HWX2 #HXW2 #H21 #H22 #H11 #H12 destruct -IH2
<minus_O_n <minus_n_O
@(cnv_cpm_conf_lpr_atom_ell_aux … IH1) -IH1 /1 width=6 by/
- | #H21 #H22 #s1 #H11 #H12 #H13 destruct -L -a -o
+ | #H21 #H22 #s1 #H11 #H12 #H13 destruct -a -L
<minus_O_n <minus_n_O
/3 width=1 by cnv_cpm_conf_lpr_atom_ess_aux, ex2_commute/
- | #s2 #H21 #H22 #H23 #s1 #H11 #H12 #H13 destruct -L -a -o
+ | #s2 #H21 #H22 #H23 #s1 #H11 #H12 #H13 destruct -a -L
<minus_n_n
/2 width=1 by cnv_cpm_conf_lpr_atom_atom_aux/
| #K2 #V2 #XV2 #i2 #_ #_ #_ #H21 #s1 #H11 #H12 #H13 destruct
| #s2 #H21 #H22 #H23 #K1 #V1 #XV1 #i1 #_ #_ #_ #H11 destruct
| #K2 #V2 #XV2 #i2 #HLK2 #HVX2 #HXV2 #H21 #K1 #V1 #XV1 #i1 #HLK1 #HVX1 #HXV1 #H11 destruct -IH2
@(cnv_cpm_conf_lpr_delta_delta_aux … IH1) -IH1 /1 width=13 by/
- | #m2 #K2 #W2 #XW2 #i2 #HLK2 #_ #_ #H21 #H22 #K1 #V1 #XV1 #i1 #HLK1 #_ #_ #H11 destruct -a -o -XW2 -XV1 -HL2 -HL1
+ | #m2 #K2 #W2 #XW2 #i2 #HLK2 #_ #_ #H21 #H22 #K1 #V1 #XV1 #i1 #HLK1 #_ #_ #H11 destruct -a -XW2 -XV1 -HL2 -HL1
elim cnv_cpm_conf_lpr_delta_ell_aux /1 width=8 by/
- | #H21 #H22 #m1 #K1 #W1 #XW1 #i1 #HLK1 #HWX1 #HXW1 #H11 #H12 destruct -IH2
+ | #H21 #H22 #m1 #K1 #W1 #XW1 #i1 #HLK1 #HWX1 #HXW1 #H11 #H12 destruct -IH2
<minus_O_n <minus_n_O
@ex2_commute @(cnv_cpm_conf_lpr_atom_ell_aux … IH1) -IH1 /1 width=6 by/
| #s2 #H21 #H22 #H23 #m1 #K1 #W1 #XW1 #i1 #_ #_ #_ #H11 #H12 destruct
- | #K2 #V2 #XV2 #i2 #HLK2 #_ #_ #H21 #m1 #K1 #W1 #XW1 #i1 #HLK1 #_ #_ #H11 #H12 destruct -a -o -XV2 -XW1 -HL2 -HL1
+ | #K2 #V2 #XV2 #i2 #HLK2 #_ #_ #H21 #m1 #K1 #W1 #XW1 #i1 #HLK1 #_ #_ #H11 #H12 destruct -a -XV2 -XW1 -HL2 -HL1
elim cnv_cpm_conf_lpr_delta_ell_aux /1 width=8 by/
| #m2 #K2 #W2 #XW2 #i2 #HLK2 #HWX2 #HXW2 #H21 #H22 #m1 #K1 #W1 #XW1 #i1 #HLK1 #HWX1 #HXW1 #H11 #H12 destruct -IH2
>minus_S_S >minus_S_S
projects / helm.git / blobdiff