lemma cpms_tneqx_fwd_fpbg (h) (n):
∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ➡*[h,n] T2 →
- (T1 ≛ T2 → ⊥) → ❪G,L,T1❫ >[h] ❪G,L,T2❫.
-/3 width=2 by cpms_fwd_cpxs, cpxs_tneqx_fpbg/ qed-.
+ (T1 ≛ T2 → ⊥) → ❪G,L,T1❫ > ❪G,L,T2❫.
+/3 width=3 by cpms_fwd_cpxs, cpxs_tneqx_fpbg/ qed-.
lemma fpbg_cpms_trans (h) (n):
- ∀G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ >[h] ❪G2,L2,T❫ →
- ∀T2. ❪G2,L2❫ ⊢ T ➡*[h,n] T2 → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
+ ∀G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ > ❪G2,L2,T❫ →
+ ∀T2. ❪G2,L2❫ ⊢ T ➡*[h,n] T2 → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
/3 width=5 by fpbg_fpbs_trans, cpms_fwd_fpbs/ qed-.
lemma cpms_fpbg_trans (h) (n):
∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ➡*[h,n] T →
- ∀G2,L2,T2. ❪G1,L1,T❫ >[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
+ ∀G2,L2,T2. ❪G1,L1,T❫ > ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
/3 width=5 by fpbs_fpbg_trans, cpms_fwd_fpbs/ qed-.
lemma fqup_cpms_fwd_fpbg (h):
∀G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ ⬂+ ❪G2,L2,T❫ →
- ∀n,T2. ❪G2,L2❫ ⊢ T ➡*[h,n] T2 → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
+ ∀n,T2. ❪G2,L2❫ ⊢ T ➡*[h,n] T2 → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
/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):
∀n1,T. ❪G,L❫ ⊢ T1 ➡[h,n1] T → (T1 ≛ T → ⊥) →
- ∀n2,T2. ❪G,L❫⊢ T ➡*[h,n2] T2 → T1 ≛ T2 → ❪G,L,T1❫ >[h] ❪G,L,T1❫.
+ ∀n2,T2. ❪G,L❫⊢ T ➡*[h,n2] T2 → T1 ≛ 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-.