milestone update in ground_2 and basic_2A

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpbc.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpbc.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpbc.etc
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+lemma fpb_fpbc_or_fpn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
+                       ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ ∨
+                       ⦃G1, L1, T1⦄ ⊢ ➡[h,g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+/3 width=1 by and3_intro, or_intror/
+[ #G2 #L2 #T2 #H elim (fquq_inv_gen … H) -H [| * ]
+  /3 width=1 by fpbc_fqu, and3_intro, or_introl, or_intror/
+| #T2 #HT12 elim (eq_term_dec T1 T2) #H destruct
+  /4 width=1 by and3_intro, or_introl, or_intror, fpbc_cpx/
+]
+qed-.
+
+lemma fpb_fpbc: ∀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 #H0 elim (fpb_fpbc_or_fpn … H) -H //
+#H elim H0 -H0 /2 width=3 by fpn_fwd_bteq/
+qed.
+
+lemma fpbc_fwd_bteq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
+                     ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⊥.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=8 by fqu_fwd_bteq/
+#T2 #_ #HT12 * /2 width=1 by/
+qed-.