/3 width=2 by cpms_fwd_cpxs, cpxs_tdneq_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 ➡*[n,h] T2 → ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
+ ∀G1,G2,L1,L2,T1,T. ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T⦄ →
+ ∀T2. ⦃G2,L2⦄ ⊢ T ➡*[n,h] T2 → ⦃G1,L1,T1⦄ >[h] ⦃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 ➡*[n,h] T →
- ∀G2,L2,T2. ⦃G1, L1, T⦄ >[h] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
+ ∀G1,L1,T1,T. ⦃G1,L1⦄ ⊢ T1 ➡*[n,h] T →
+ ∀G2,L2,T2. ⦃G1,L1,T⦄ >[h] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ >[h] ⦃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 ➡*[n,h] T2 → ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
-/3 width=5 by cpms_fwd_fpbs, fqup_fpbg,fpbg_fpbs_trans/ qed-.
+ ∀G1,G2,L1,L2,T1,T. ⦃G1,L1,T1⦄ ⬂+ ⦃G2,L2,T⦄ →
+ ∀n,T2. ⦃G2,L2⦄ ⊢ T ➡*[n,h] T2 → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
+/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):
∀n1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → (T1 ≛ T → ⊥) →