- lambda_delta: context-free weak head normal forms continued ...

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / reducibility / twhnf.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/twhnf.ma b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/twhnf.ma
index c96bf4762f1316c07a6e1b80b8ec54b826c4e100..dea7077b494eafd17e09fc2798bd20e964b3e066 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/twhnf.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/twhnf.ma
@@ -1,12 +1,57 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "Basic_2/grammar/thom.ma".
 include "Basic_2/reducibility/tpr.ma".
 
 (* CONTEXT-FREE WEAK HEAD NORMAL TERMS **************************************)
 
 definition twhnf: term → Prop ≝
-   NF … tpr (thom …).
+   NF … tpr thom.
 
 interpretation
    "context-free weak head normality (term)"
    'WHdNormal T = (twhnf T).
 
+(* Basic inversion lemmas ***************************************************)
+
+lemma twhnf_inv_thom: ∀T. 𝕎ℍℕ[T] → T ≈ T.
+normalize /2 depth=1/
+qed-.
+
 (* Basic properties *********************************************************)
+
+lemma tpr_thom: ∀T1,T2. T1 ⇒ T2 → T1 ≈ T1 → T1 ≈ T2.
+#T1 #T2 #H elim H -T1 T2 //
+[ #I #V1 #V2 #T1 #T2 #_ #_ #_ #IHT12 #H
+  elim (thom_inv_flat1 … H) -H #W2 #U2 #HT1U2 #HT1 #_ #H1 #H2 destruct -I T1 V1;
+  lapply (IHT12 HT1U2) -IHT12 HT1U2 #HUT2
+  lapply (simple_thom_repl_dx … HUT2 HT1) /2 width=1/
+| #V1 #V2 #W #T1 #T2 #_ #_ #_ #_ #H
+  elim (thom_inv_flat1 … H) -H #W2 #U2 #_ #H
+  elim (simple_inv_bind … H)
+| #I #V1 #V2 #T1 #T #T2 #_ #_ #_ #_ #_ #H
+  elim (thom_inv_bind1 … H) -H #W2 #U2 #H destruct -I //
+| #V2 #V1 #V #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
+  elim (thom_inv_flat1 … H) -H #U1 #U2 #_ #H
+  elim (simple_inv_bind … H)
+| #V #T #T1 #T2 #_ #_ #_ #H
+  elim (thom_inv_bind1 … H) -H #W2 #U2 #H destruct
+| #V #T1 #T2 #_ #_ #H
+  elim (thom_inv_flat1 … H) -H #W2 #U2 #_ #_ #_ #H destruct
+]
+qed.
+
+lemma twhnf_thom: ∀T. T ≈ T → 𝕎ℍℕ[T].
+/2/ qed.