(* *)
(**************************************************************************)
-include "ground_2/lib/arith_2b.ma".
+include "ground/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_cpms.ma".
(* 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} â\9e¡*[O,h] T.
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93ª[I] â\9e¡*[h,0] T & â\9d¨G,L2â\9d© â\8a¢ â\93ª[I] â\9e¡*[h,0] 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) â\9e¡*[h] T.
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\8b\86s â\9e¡*[h,1] T & â\9d¨G,L2â\9d© â\8a¢ â\8b\86(⫯[h]s) â\9e¡*[h,0] T.
/3 width=3 by cpm_cpms, ex2_intro/ qed-.
-fact cnv_cpm_conf_lpr_atom_delta_aux (a) (h) (G) (L) (i):
- (â\88\80G0,L0,T0. â¦\83G,L,#iâ¦\84 >[h] 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 â\8a¢ V â\9e¡[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 â\8a¢ â\9e¡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ #i â\9e¡*[n,h] T & â¦\83G,L2â¦\84 â\8a¢ X â\9e¡*[h] T.
-#a #h #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\9d¨G,L,#iâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d©â\8a¢#i![h,a] →
+ â\88\80K,V. â\87©[i]L ≘ K.ⓓV →
+ â\88\80n,XV. â\9d¨G,Kâ\9d© â\8a¢ V â\9e¡[h,n] XV →
+ â\88\80X. â\87§[↑i]XV ≘ X →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ #i â\9e¡*[h,n] T & â\9d¨G,L2â\9d© â\8a¢ X â\9e¡*[h,0] 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
/3 width=6 by cpms_delta_drops, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_atom_ell_aux (a) (h) (G) (L) (i):
- (â\88\80G0,L0,T0. â¦\83G,L,#iâ¦\84 >[h] 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 â\8a¢ W â\9e¡[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 â\8a¢ â\9e¡[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 â\8a¢ X â\9e¡*[h] T.
-#a #h #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\9d¨G,L,#iâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d©â\8a¢#i![h,a] →
+ â\88\80K,W. â\87©[i]L ≘ K.ⓛW →
+ â\88\80n,XW. â\9d¨G,Kâ\9d© â\8a¢ W â\9e¡[h,n] XW →
+ â\88\80X. â\87§[↑i]XW ≘ X →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ #i â\9e¡*[h,â\86\91n] T & â\9d¨G,L2â\9d© â\8a¢ X â\9e¡*[h,0] 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
/3 width=6 by cpms_ell_drops, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_delta_delta_aux (a) (h) (I) (G) (L) (i):
- (â\88\80G0,L0,T0. â¦\83G,L,#iâ¦\84 >[h] 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 â\8a¢ V2 â\9e¡[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 â\8a¢ â\9e¡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ X1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 â\8a¢ X2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,#iâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,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\9d¨G,K1â\9d© â\8a¢ V1 â\9e¡[h,n1] XV1 â\86\92 â\88\80n2,XV2. â\9d¨G,K2â\9d© â\8a¢ V2 â\9e¡[h,n2] 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\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ X1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ X2 â\9e¡*[h,n1-n2] 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
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) (p) (I) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\91{p,I}V.Tâ¦\84 >[h] 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 â\8a¢ V â\9e¡[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 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[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 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\91[p,I]V.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\91[p,I]V.T ![h,a] →
+ â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V2 →
+ â\88\80n1,T1. â\9d¨G,L.â\93\91[I]Vâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\91[I]Vâ\9d© â\8a¢ T â\9e¡[h,n2] T2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\91[p,I]V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ â\93\91[p,I]V2.T2 â\9e¡*[h,n1-n2] 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_sub … 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) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,+â\93\93V.Tâ¦\84 >[h] 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 â\8a¢ T2 â\9e¡[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 â\8a¢ â\9e¡[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 â\8a¢ XT2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,+â\93\93V.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ +â\93\93V.T ![h,a] →
+ â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢V â\9e¡[h,0] V1 â\86\92 â\88\80n1,T1. â\9d¨G,L.â\93\93Vâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92
+ â\88\80T2. â\87§[1]T2 â\89\98 T â\86\92 â\88\80n2,XT2. â\9d¨G,Lâ\9d© â\8a¢ T2 â\9e¡[h,n2] XT2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ +â\93\93V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ XT2 â\9e¡*[h,n1-n2] 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_sub … IH … HXT12 … HXT2 … HL01 … HL02)
/3 width=3 by cpms_zeta, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_zeta_zeta_aux (a) (h) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,+â\93\93V.Tâ¦\84 >[h] 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 â\8a¢ T2 â\9e¡[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 â\8a¢ â\9e¡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ XT1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 â\8a¢ XT2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,+â\93\93V.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,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\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡[h,n1] XT1 â\86\92 â\88\80n2,XT2. â\9d¨G,Lâ\9d© â\8a¢ T2 â\9e¡[h,n2] XT2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ XT1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ XT2 â\9e¡*[h,n1-n2] 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
/2 width=3 by ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_appl_appl_aux (a) (h) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\90V.Tâ¦\84 >[h] 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 â\8a¢ V â\9e¡[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 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[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\90V2.T2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\90V.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\90V.T ![h,a] →
+ â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V2 →
+ â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n2] T2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\90V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ â\93\90V2.T2 â\9e¡*[h,n1-n2] 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
/3 width=5 by cpms_appl_dx, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_appl_beta_aux (a) (h) (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] 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 â\8a¢ V â\9e¡[h] V2 →
- â\88\80W2. â¦\83G,Lâ¦\84 â\8a¢ W â\9e¡[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 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[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}â\93\9dW2.V2.T2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\90V.â\93\9b[p]W.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\90V.â\93\9b[p]W.T ![h,a] →
+ â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V2 →
+ â\88\80W2. â\9d¨G,Lâ\9d© â\8a¢ W â\9e¡[h,0] W2 →
+ â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ â\93\9b[p]W.T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\9bWâ\9d© â\8a¢ T â\9e¡[h,n2] T2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\90V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ â\93\93[p]â\93\9dW2.V2.T2 â\9e¡*[h,n1-n2] 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
/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) (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] 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 â\8a¢ V â\9e¡[h] V2 →
- â\88\80W2. â¦\83G,Lâ¦\84 â\8a¢ W â\9e¡[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 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[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.â\93\90U2.T2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\90V.â\93\93[p]W.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\90V.â\93\93[p]W.T ![h,a] →
+ â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V2 →
+ â\88\80W2. â\9d¨G,Lâ\9d© â\8a¢ W â\9e¡[h,0] W2 →
+ â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ â\93\93[p]W.T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\93Wâ\9d© â\8a¢ T â\9e¡[h,n2] T2 →
+ â\88\80U2. â\87§[1]V2 ≘ U2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\90V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ â\93\93[p]W2.â\93\90U2.T2 â\9e¡*[h,n1-n2] 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
#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_sub … IH … H1X0 … HX02 … HL01 … HL02)
[|*: /4 width=5 by fqup_fpbg, fqup_strap1, fqu_drop/ ] #T #HT1 #HT2 -L0 -V0 -W0 -T0
]
qed-.
-fact cnv_cpm_conf_lpr_beta_beta_aux (a) (h) (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] 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 â\8a¢ V â\9e¡[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 â\8a¢ W â\9e¡[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 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[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}â\93\9dW2.V2.T2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\90V.â\93\9b[p]W.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\90V.â\93\9b[p]W.T ![h,a] →
+ â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V2 →
+ â\88\80W1. â\9d¨G,Lâ\9d© â\8a¢ W â\9e¡[h,0] W1 â\86\92 â\88\80W2. â\9d¨G,Lâ\9d© â\8a¢ W â\9e¡[h,0] W2 →
+ â\88\80n1,T1. â\9d¨G,L.â\93\9bWâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\9bWâ\9d© â\8a¢ T â\9e¡[h,n2] T2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\93[p]â\93\9dW1.V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ â\93\93[p]â\93\9dW2.V2.T2 â\9e¡*[h,n1-n2] 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
/4 width=5 by cpms_bind_dx, cpm_eps, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_theta_theta_aux (a) (h) (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] 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 â\8a¢ V â\9e¡[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 â\8a¢ W â\9e¡[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 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[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.â\93\90U2.T2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\90V.â\93\93[p]W.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\90V.â\93\93[p]W.T ![h,a] →
+ â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V2 →
+ â\88\80W1. â\9d¨G,Lâ\9d© â\8a¢ W â\9e¡[h,0] W1 â\86\92 â\88\80W2. â\9d¨G,Lâ\9d© â\8a¢ W â\9e¡[h,0] W2 →
+ â\88\80n1,T1. â\9d¨G,L.â\93\93Wâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\93Wâ\9d© â\8a¢ T â\9e¡[h,n2] 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\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\93[p]W1.â\93\90U1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ â\93\93[p]W2.â\93\90U2.T2 â\9e¡*[h,n1-n2] 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
/4 width=7 by cpms_appl_dx, cpms_bind_dx, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_cast_cast_aux (a) (h) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h] 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 â\8a¢ V â\9e¡[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 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[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 â\8a¢ â\93\9dV2.T2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n1] V1 â\86\92 â\88\80n2,V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n2] V2 →
+ â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n2] T2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\9dV1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ â\93\9dV2.T2 â\9e¡*[h,n1-n2] 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
/3 width=5 by cpms_cast, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_cast_epsilon_aux (a) (h) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h] 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\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 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[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 â\8a¢ T2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n1] V1 →
+ â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n2] T2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\9dV1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ T2 â\9e¡*[h,n1-n2] 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
/3 width=3 by cpms_eps, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_cast_ee_aux (a) (h) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h] 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] 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 â\8a¢ V â\9e¡[n2,h] V2 →
- â\88\80T1. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[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 â\8a¢ V2 â\9e¡*[n1-â\86\91n2,h] T.
-#a #h #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\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
+ (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n1] V1 â\86\92 â\88\80n2,V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n2] V2 →
+ â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\9dV1.T1 â\9e¡*[h,â\86\91n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ V2 â\9e¡*[h,n1-â\86\91n2] 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
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/ ]
+elim (IH1 … HV1 … HT2 … HL02 … HL01) [|*: /2 width=5 by fqup_cpms_fwd_fpbg/ ]
-L0 -V0 -T0 -X0 #U #HVU #HTU
lapply (cpms_trans … HV2 … HVU) -V <plus_O_n >minus_plus #H2
lapply (cpms_trans … HT1 … HTU) -T <arith_l2 #H1
/3 width=3 by cpms_eps, ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_epsilon_epsilon_aux (a) (h) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h] 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 â\8a¢ T â\9e¡[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 â\8a¢ â\9e¡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ T1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 â\8a¢ T2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n2] T2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ T2 â\9e¡*[h,n1-n2] 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
/2 width=3 by ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_epsilon_ee_aux (a) (h) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h] 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] 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 â\8a¢ V â\9e¡[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 â\8a¢ â\9e¡[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 â\8a¢ V2 â\9e¡*[n1-â\86\91n2,h] T.
-#a #h #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\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
+ (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n2] V2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ T1 â\9e¡*[h,â\86\91n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ V2 â\9e¡*[h,n1-â\86\91n2] 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
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/ ]
+elim (IH1 … HV1 … HT2 … HL02 … HL01) [|*: /2 width=5 by fqup_cpms_fwd_fpbg/ ]
-L0 -V0 -T0 -X0 #U #HVU #HTU
lapply (cpms_trans … HV2 … HVU) -V <plus_O_n >minus_plus #H2
lapply (cpms_trans … HT1 … HTU) -T <arith_l2 #H1
/2 width=3 by ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_ee_ee_aux (a) (h) (G) (L) (V) (T):
- (â\88\80G0,L0,T0. â¦\83G,L,â\93\9dV.Tâ¦\84 >[h] 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 â\8a¢ V â\9e¡[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 â\8a¢ â\9e¡[h] L2 →
- â\88\83â\88\83T. â¦\83G,L1â¦\84 â\8a¢ V1 â\9e¡*[n2-n1,h] T & â¦\83G,L2â¦\84 â\8a¢ V2 â\9e¡*[n1-n2,h] T.
-#a #h #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\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© â\86\92 IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+ â\9d¨G,Lâ\9d© â\8a¢ â\93\9dV.T ![h,a] →
+ â\88\80n1,V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n1] V1 â\86\92 â\88\80n2,V2. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n2] V2 →
+ â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ V1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© â\8a¢ V2 â\9e¡*[h,n1-n2] 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
/2 width=3 by ex2_intro/
qed-.
-fact cnv_cpm_conf_lpr_aux (a) (h):
- ∀G0,L0,T0.
- (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) →
- (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h] ⦃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 #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
+fact cnv_cpm_conf_lpr_aux (h) (a):
+ ∀G0,L0,T0.
+ (∀G1,L1,T1. ❨G0,L0,T0❩ > ❨G1,L1,T1❩ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
+ (∀G1,L1,T1. ❨G0,L0,T0❩ > ❨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 *
@(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 -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