(* Forward lemmas with proper parallel rst-computation for closures *********)
-lemma cpms_tdneq_fwd_fpbg (h) (n):
- â\88\80G,L,T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 →
- (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 â¦\83G,L,T1â¦\84 >[h] â¦\83G,L,T2â¦\84.
-/3 width=2 by cpms_fwd_cpxs, cpxs_tdneq_fpbg/ qed-.
+lemma cpms_tneqx_fwd_fpbg (h) (n):
+ â\88\80G,L,T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n] T2 →
+ (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 â\9dªG,L,T1â\9d« >[h] â\9dªG,L,T2â\9d«.
+/3 width=2 by cpms_fwd_cpxs, cpxs_tneqx_fpbg/ qed-.
lemma fpbg_cpms_trans (h) (n):
- â\88\80G1,G2,L1,L2,T1,T. â¦\83G1, L1, T1â¦\84 >[h] â¦\83G2, L2, Tâ¦\84 →
- â\88\80T2. â¦\83G2, L2â¦\84 â\8a¢ T â\9e¡*[n,h] T2 â\86\92 â¦\83G1, L1, T1â¦\84 >[h] â¦\83G2, L2, T2â¦\84.
+ â\88\80G1,G2,L1,L2,T1,T. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,Tâ\9d« →
+ â\88\80T2. â\9dªG2,L2â\9d« â\8a¢ T â\9e¡*[h,n] T2 â\86\92 â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
/3 width=5 by fpbg_fpbs_trans, cpms_fwd_fpbs/ qed-.
lemma cpms_fpbg_trans (h) (n):
- â\88\80G1,L1,T1,T. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[n,h] T →
- â\88\80G2,L2,T2. â¦\83G1, L1, Tâ¦\84 >[h] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >[h] â¦\83G2, L2, T2â¦\84.
+ â\88\80G1,L1,T1,T. â\9dªG1,L1â\9d« â\8a¢ T1 â\9e¡*[h,n] T →
+ â\88\80G2,L2,T2. â\9dªG1,L1,Tâ\9d« >[h] â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
/3 width=5 by fpbs_fpbg_trans, cpms_fwd_fpbs/ qed-.
lemma fqup_cpms_fwd_fpbg (h):
- â\88\80G1,G2,L1,L2,T1,T. â¦\83G1, L1, T1â¦\84 â\8a\90+ â¦\83G2, L2, Tâ¦\84 →
- â\88\80n,T2. â¦\83G2, L2â¦\84 â\8a¢ T â\9e¡*[n,h] T2 â\86\92 â¦\83G1, L1, T1â¦\84 >[h] â¦\83G2, L2, T2â¦\84.
-/3 width=5 by cpms_fwd_fpbs, fqup_fpbg,fpbg_fpbs_trans/ qed-.
+ â\88\80G1,G2,L1,L2,T1,T. â\9dªG1,L1,T1â\9d« â¬\82+ â\9dªG2,L2,Tâ\9d« →
+ â\88\80n,T2. â\9dªG2,L2â\9d« â\8a¢ T â\9e¡*[h,n] T2 â\86\92 â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
+/3 width=5 by cpms_fwd_fpbs, fqup_fpbg, fpbg_fpbs_trans/ qed-.
-lemma cpm_tdneq_cpm_cpms_tdeq_sym_fwd_fpbg (h) (G) (L) (T1):
- â\88\80n1,T. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡[n1,h] T → (T1 ≛ T → ⊥) →
- â\88\80n2,T2. â¦\83G,Lâ¦\84â\8a¢ T â\9e¡*[n2,h] T2 â\86\92 T1 â\89\9b T2 â\86\92 â¦\83G,L,T1â¦\84 >[h] â¦\83G,L,T1â¦\84.
+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 → (T1 ≛ 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 â\86\92 â\9dªG,L,T1â\9d« >[h] â\9dªG,L,T1â\9d«.
#h #G #L #T1 #n1 #T #H1T1 #H2T1 #n2 #T2 #H1T2 #H2T12
-/4 width=7 by cpms_fwd_fpbs, cpm_fpb, fpbs_tdeq_trans, tdeq_sym, ex2_3_intro/
+/4 width=7 by cpms_fwd_fpbs, cpm_fpb, fpbs_teqx_trans, teqx_sym, ex2_3_intro/
qed-.