milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / fpn / fpbs_conj.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpbs_conj.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpbs_conj.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpbs_conj.etc
@@ -0,0 +1,34 @@
+(*
+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
+*)