(* Sub confluence propery with restricted rt-transition for terms ***********)
fact cnv_cpms_teqx_strip_lpr_aux (h) (a) (G0) (L0) (T0):
- (â\88\80G,L,T. â\9dªG0,L0,T0â\9d« > â\9dªG,L,Tâ\9d« → IH_cnv_cpm_trans_lpr h a G L T) →
- (â\88\80G,L,T. â\9dªG0,L0,T0â\9d« > â\9dªG,L,Tâ\9d« → 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« ⊢ T0 ![h,a] → T0 ≅ T1 →
- â\88\80n2,T2. â\9dªG0,L0â\9d« ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
- â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
- 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« ⊢ T2 ➡*[h,n1-n2] T & T2 ≅ T.
+ (â\88\80G,L,T. â\9d¨G0,L0,T0â\9d© > â\9d¨G,L,Tâ\9d© → IH_cnv_cpm_trans_lpr h a G L T) →
+ (â\88\80G,L,T. â\9d¨G0,L0,T0â\9d© > â\9d¨G,L,Tâ\9d© → IH_cnv_cpms_conf_lpr h a G L T) →
+ â\88\80n1,T1. â\9d¨G0,L0â\9d© â\8a¢ T0 â\9e¡*[h,n1] T1 â\86\92 â\9d¨G0,L0â\9d© ⊢ T0 ![h,a] → T0 ≅ T1 →
+ â\88\80n2,T2. â\9d¨G0,L0â\9d© ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
+ â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ T1 â\9e¡[h,n2-n1] T & T1 â\89\85 T & â\9d¨G0,L2â\9d© ⊢ T2 ➡*[h,n1-n2] T & T2 ≅ 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
qed-.
fact cnv_cpms_teqx_conf_lpr_aux (h) (a) (G0) (L0) (T0):
- (â\88\80G,L,T. â\9dªG0,L0,T0â\9d« > â\9dªG,L,Tâ\9d« → IH_cnv_cpm_trans_lpr h a G L T) →
- (â\88\80G,L,T. â\9dªG0,L0,T0â\9d« > â\9dªG,L,Tâ\9d« → 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« ⊢ T0 ![h,a] → T0 ≅ T1 →
- â\88\80n2,T2. â\9dªG0,L0â\9d« ⊢ T0 ➡*[h,n2] T2 → T0 ≅ T2 →
- â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
- 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« ⊢ T2 ➡*[h,n1-n2] T & T2 ≅ T.
+ (â\88\80G,L,T. â\9d¨G0,L0,T0â\9d© > â\9d¨G,L,Tâ\9d© → IH_cnv_cpm_trans_lpr h a G L T) →
+ (â\88\80G,L,T. â\9d¨G0,L0,T0â\9d© > â\9d¨G,L,Tâ\9d© → IH_cnv_cpms_conf_lpr h a G L T) →
+ â\88\80n1,T1. â\9d¨G0,L0â\9d© â\8a¢ T0 â\9e¡*[h,n1] T1 â\86\92 â\9d¨G0,L0â\9d© ⊢ T0 ![h,a] → T0 ≅ T1 →
+ â\88\80n2,T2. â\9d¨G0,L0â\9d© ⊢ T0 ➡*[h,n2] T2 → T0 ≅ T2 →
+ â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+ â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ T1 â\9e¡*[h,n2-n1] T & T1 â\89\85 T & â\9d¨G0,L2â\9d© ⊢ T2 ➡*[h,n1-n2] T & T2 ≅ 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
#n2 #T2 #H1T02 #H2T02 #L1 #HL01 #L2 #HL02
elim (cnv_cpms_teqx_strip_lpr_aux … IH2 IH1 … H1T02 H0T0 H2T02 … H1T03 H2T03 … HL02 L0) -H0T0 -H2T03 //
#T4 #H1T24 #H2T24 #H1T34 #H2T34
- elim (IH … H1T34 H2T34 … HL01 … HL02) [|*: /4 width=5 by cpm_fpbq, fpbq_fpbg_trans/ ] -L0 -T0 -T3 (**)
+ elim (IH … H1T34 H2T34 … HL01 … HL02) [|*: /4 width=5 by cpm_fwd_fpb, fpb_fpbg_trans/ ] -L0 -T0 -T3 (**)
#T3 #H1T13 #H2T13 #H1T43 #H2T43
<minus_plus >arith_l3
/3 width=7 by cpms_step_sn, teqx_trans, ex4_intro/