(*
inclade "basic_2/computation/fpns.ma".
inclade "basic_2/computation/fpbs.ma".
inclade "basic_2/reduction/fpbc.ma".

lemma fpn_dec: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
               Decidable (⦃G1, L1, T1⦄ ⊢ ➡[h, g] ⦃G2, L2, T2⦄).
#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fpb_fpbc_or_fpn … H) -H /2 width=1 by or_introl/
#H12 @or_intror
#H @(fpbc_fwd_bteq … H12) -H12 @(fpn_fwd_bteq … H)
qed-.
*)
(*
lemma fpns_dec: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
                Decidable (⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄).
#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2 /2 width=1 by or_introl/
#G #G2 #L #L2 #T #T2 #H #H2 *
#H1 elim (fpn_dec … H2) -H2 #H2 /3 width=5 by fpns_strap1, or_introl/
[ @or_intror #H12
| @or_intror #H12 @H1 -H1
*)
(*
inclade "basic_2/grammar/bteq_bteq.ma".
inclade "basic_2/computation/fpns.ma".

(* Advanced forward lemmas **************************************************)

lemma fpbs_bteq_fwd_fpns: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
                          ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄.
#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2 //
#G #G2 #L #L2 #T #T2 #H1 #H2 #IH1 #H12 elim (bteq_dec G1 G L1 L T1 T)
[ -H1 /4 width=10 by fpns_strap1, fpb_bteq_fwd_fpn, bteq_canc_sn/
| -IH1 #H
*)