fact cnv_cpms_teqx_strip_lpr_aux (h) (a) (G0) (L0) (T0):
(∀G,L,T. ❪G0,L0,T0❫ > ❪G,L,T❫ → IH_cnv_cpm_trans_lpr h a G L T) →
(∀G,L,T. ❪G0,L0,T0❫ > ❪G,L,T❫ → IH_cnv_cpms_conf_lpr h a G L T) →
- â\88\80n1,T1. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡*[h,n1] T1 â\86\92 â\9dªG0,L0â\9d« â\8a¢ T0 ![h,a] â\86\92 T0 â\89\9b T1 →
- â\88\80n2,T2. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡[h,n2] T2 â\86\92 T0 â\89\9b T2 →
+ â\88\80n1,T1. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡*[h,n1] T1 â\86\92 â\9dªG0,L0â\9d« â\8a¢ T0 ![h,a] â\86\92 T0 â\89\85 T1 →
+ â\88\80n2,T2. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡[h,n2] T2 â\86\92 T0 â\89\85 T2 →
∀L1. ❪G0,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G0,L0❫ ⊢ ➡[h,0] L2 →
- â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ T1 â\9e¡[h,n2-n1] T & T1 â\89\9b T & â\9dªG0,L2â\9d« â\8a¢ T2 â\9e¡*[h,n1-n2] T & T2 â\89\9b T.
+ â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ T1 â\9e¡[h,n2-n1] T & T1 â\89\85 T & â\9dªG0,L2â\9d« â\8a¢ T2 â\9e¡*[h,n1-n2] T & T2 â\89\85 T.
#h #a #G #L0 #T0 #IH2 #IH1 #n1 #T1 #H1T01 #H0T0 #H2T01
@(cpms_teqx_ind_sn … H1T01 H0T0 H2T01 IH1 IH2) -n1 -T0
[ #H0T1 #n2 #T2 #H1T12 #H2T12 #L1 #HL01 #L2 #HL02
fact cnv_cpms_teqx_conf_lpr_aux (h) (a) (G0) (L0) (T0):
(∀G,L,T. ❪G0,L0,T0❫ > ❪G,L,T❫ → IH_cnv_cpm_trans_lpr h a G L T) →
(∀G,L,T. ❪G0,L0,T0❫ > ❪G,L,T❫ → IH_cnv_cpms_conf_lpr h a G L T) →
- â\88\80n1,T1. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡*[h,n1] T1 â\86\92 â\9dªG0,L0â\9d« â\8a¢ T0 ![h,a] â\86\92 T0 â\89\9b T1 →
- â\88\80n2,T2. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡*[h,n2] T2 â\86\92 T0 â\89\9b T2 →
+ â\88\80n1,T1. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡*[h,n1] T1 â\86\92 â\9dªG0,L0â\9d« â\8a¢ T0 ![h,a] â\86\92 T0 â\89\85 T1 →
+ â\88\80n2,T2. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡*[h,n2] T2 â\86\92 T0 â\89\85 T2 →
∀L1. ❪G0,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G0,L0❫ ⊢ ➡[h,0] L2 →
- â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ T1 â\9e¡*[h,n2-n1] T & T1 â\89\9b T & â\9dªG0,L2â\9d« â\8a¢ T2 â\9e¡*[h,n1-n2] T & T2 â\89\9b T.
+ â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ T1 â\9e¡*[h,n2-n1] T & T1 â\89\85 T & â\9dªG0,L2â\9d« â\8a¢ T2 â\9e¡*[h,n1-n2] T & T2 â\89\85 T.
#h #a #G #L0 #T0 #IH2 #IH1 #n1 #T1 #H1T01 #H0T0 #H2T01
generalize in match IH1; generalize in match IH2;
@(cpms_teqx_ind_sn … H1T01 H0T0 H2T01 IH1 IH2) -n1 -T0