lemma cpms_tneqx_fwd_fpbg (h) (n):
∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ➡*[h,n] T2 →
- (T1 â\89\9b T2 → ⊥) → ❪G,L,T1❫ > ❪G,L,T2❫.
+ (T1 â\89\85 T2 → ⊥) → ❪G,L,T1❫ > ❪G,L,T2❫.
/3 width=3 by cpms_fwd_cpxs, cpxs_tneqx_fpbg/ qed-.
lemma fpbg_cpms_trans (h) (n):
/3 width=5 by cpms_fwd_fpbs, fqup_fpbg, fpbg_fpbs_trans/ qed-.
lemma cpm_tneqx_cpm_cpms_teqx_sym_fwd_fpbg (h) (G) (L) (T1):
- â\88\80n1,T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h,n1] T â\86\92 (T1 â\89\9b T → ⊥) →
- â\88\80n2,T2. â\9dªG,Lâ\9d«â\8a¢ T â\9e¡*[h,n2] T2 â\86\92 T1 â\89\9b T2 → ❪G,L,T1❫ > ❪G,L,T1❫.
+ â\88\80n1,T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h,n1] T â\86\92 (T1 â\89\85 T → ⊥) →
+ â\88\80n2,T2. â\9dªG,Lâ\9d«â\8a¢ T â\9e¡*[h,n2] T2 â\86\92 T1 â\89\85 T2 → ❪G,L,T1❫ > ❪G,L,T1❫.
#h #G #L #T1 #n1 #T #H1T1 #H2T1 #n2 #T2 #H1T2 #H2T12
/4 width=7 by cpms_fwd_fpbs, cpm_fpb, fpbs_teqx_trans, teqx_sym, ex2_3_intro/
qed-.