(**************************************************************************)
include "basic_2/rt_computation/fpbg_fqup.ma".
-include "basic_2/rt_computation/fpbg_fpbs.ma".
+include "basic_2/rt_computation/fpbg_cpxs.ma".
include "basic_2/rt_computation/cpms_fpbs.ma".
(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
(* Forward lemmas with proper parallel rst-computation for closures *********)
-lemma fqup_cpms_fwd_fpbg (h) (o): ∀G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T⦄ →
- ∀n,T2. ⦃G2, L2⦄ ⊢ T ➡*[n,h] T2 → ⦃G1, L1, T1⦄ >[h,o] ⦃G2, L2, T2⦄.
-/3 width=5 by cpms_fwd_fpbs, fqup_fpbg,fpbg_fpbs_trans/ qed-.
+lemma cpms_tdneq_fwd_fpbg (h) (n):
+ ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 →
+ (T1 ≛ T2 → ⊥) → ⦃G,L,T1⦄ >[h] ⦃G,L,T2⦄.
+/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⦄.
+/3 width=5 by fpbg_fpbs_trans, cpms_fwd_fpbs/ qed-.
-lemma cpms_fpbg_trans (h) (o) (n): ∀G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ➡*[n,h] T →
- ∀G2,L2,T2. ⦃G1, L1, T⦄ >[h,o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h,o] ⦃G2, L2, T2⦄.
+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⦄.
/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-.
+
+lemma cpm_tdneq_cpm_cpms_tdeq_sym_fwd_fpbg (h) (G) (L) (T1):
+ ∀n1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → (T1 ≛ T → ⊥) →
+ ∀n2,T2. ⦃G,L⦄⊢ T ➡*[n2,h] T2 → T1 ≛ T2 → ⦃G,L,T1⦄ >[h] ⦃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_tdeq_trans, tdeq_sym, ex2_3_intro/
+qed-.