- bug fix in the induction for the closure property

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / fpbc.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbc.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbc.ma
index c560a1ab07c6383342d863db47dab2bc1036d9af..45e671601a94511c930061b812f5c5be14089584 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbc.ma
@@ -32,25 +32,6 @@ lemma cpr_fpbc: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → (T1 = T2 → ⊥)
                 ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
 /3 width=1 by fpbc_cpx, cpr_cpx/ qed.
 
-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 (term_eq_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.
-
 (* Basic forward lemmas *****************************************************)
 
 lemma fpbc_fwd_fpb: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
@@ -58,9 +39,3 @@ lemma fpbc_fwd_fpb: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2,
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
 /3 width=1 by fpb_fquq, fpb_cpx, fqu_fquq/
 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-.