- 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 ec64bd5a6642ae4fd5bab4b6a122c0fc0af842e1..45e671601a94511c930061b812f5c5be14089584 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbc.ma
@@ -13,7 +13,6 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/btpredproper_8.ma".
-include "basic_2/relocation/fquq_alt.ma".
 include "basic_2/reduction/fpb.ma".
 
 (* "BIG TREE" PROPER PARALLEL REDUCTION FOR CLOSURES ************************)
@@ -33,26 +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_refl: ∀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 = G2 & ⦃G1, L1⦄ ⊢ ➡[h, g] L2 & T1 = 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| = |G2| → |L1| = |L2| → T1 = T2 → ⊥) →
-                ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #H0 elim (fpb_fpbc_or_refl … H) -H // *
-#HG #HL #HT destruct lapply (lpx_fwd_length … HL) -HL #HL
-elim H0 -H0 //
-qed.
-
 (* Basic forward lemmas *****************************************************)
 
 lemma fpbc_fwd_fpb: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
@@ -60,9 +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_gen: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
-                    |G1| = |G2| → |L1| = |L2| → T1 = T2 → ⊥.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by /
-#G2 #L2 #T2 #H #HG #HL #HT @(fqu_fwd_gen … H) -H // (**) (* auto does not work *)
-qed-.