- transitivity of lenv refinement for atomic arity asignment proved! ...

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

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/tnf.ma b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/tnf.ma
index 3c0184e551a4a7a36aff4fae2264b928d0b0dab0..8c84f092c0e00cd235c1c521bf6a19a17c0f3609 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/tnf.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/tnf.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/substitution/tps_lift.ma".
-include "Basic_2/reducibility/trf.ma".
 include "Basic_2/reducibility/tpr.ma".
 
 (* CONTEXT-FREE NORMAL TERMS ************************************************)
@@ -59,58 +57,3 @@ lemma tnf_inv_cast: ∀V,T. ℕ[ⓣV.T] → False.
 #V #T #H lapply (H T ?) -H /2 width=1/ #H
 @(discr_tpair_xy_y … H)
 qed-.
-
-(* Basic properties *********************************************************)
-
-lemma tpr_tif_eq: ∀T1,T2. T1 ➡ T2 →  𝕀[T1] → T1 = T2.
-#T1 #T2 #H elim H -T1 -T2
-[ //
-| * #V1 #V2 #T1 #T2 #_ #_ #IHV1 #IHT1 #H
-  [ elim (tif_inv_appl … H) -H #HV1 #HT1 #_
-    >IHV1 -IHV1 // -HV1 >IHT1 -IHT1 //
-  | elim (tif_inv_cast … H)
-  ]
-| #V1 #V2 #W #T1 #T2 #_ #_ #_ #_ #H
-  elim (tif_inv_appl … H) -H #_ #_ #H
-  elim (simple_inv_bind … H)
-| * #V1 #V2 #T1 #T #T2 #_ #_ #HT2 #IHV1 #IHT1 #H
-  [ -HT2 -IHV1 -IHT1 elim (tif_inv_abbr … H)
-  | <(tps_inv_refl_SO2 … HT2 ?) -HT2 //
-    elim (tif_inv_abst … H) -H #HV1 #HT1
-    >IHV1 -IHV1 // -HV1 >IHT1 -IHT1 //
-  ]
-| #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
-  elim (tif_inv_appl … H) -H #_ #_ #H
-  elim (simple_inv_bind … H)
-| #V1 #T1 #T2 #T #_ #_ #_ #H
-  elim (tif_inv_abbr … H)
-| #V1 #T1 #T #_ #_ #H
-  elim (tif_inv_cast … H)
-]
-qed.
-
-theorem tif_tnf: ∀T1.  𝕀[T1] → ℕ[T1].
-/2 width=1/ qed.
-
-(* Note: this property is unusual *)
-theorem tnf_trf_false: ∀T1. ℝ[T1] → ℕ[T1] → False.
-#T1 #H elim H -T1
-[ #V #T #_ #IHV #H elim (tnf_inv_abst … H) -H /2 width=1/
-| #V #T #_ #IHT #H elim (tnf_inv_abst … H) -H /2 width=1/
-| #V #T #_ #IHV #H elim (tnf_inv_appl … H) -H /2 width=1/
-| #V #T #_ #IHV #H elim (tnf_inv_appl … H) -H /2 width=1/
-| #V #T #H elim (tnf_inv_abbr … H)
-| #V #T #H elim (tnf_inv_cast … H)
-| #V #W #T #H elim (tnf_inv_appl … H) -H #_ #_ #H
-  elim (simple_inv_bind … H)
-]
-qed.
-
-theorem tnf_tif: ∀T1. ℕ[T1] → 𝕀[T1].
-/2 width=3/ qed.
-
-lemma tnf_abst: ∀V,T. ℕ[V] → ℕ[T] → ℕ[ⓛV.T].
-/4 width=1/ qed.
-
-lemma tnf_appl: ∀V,T. ℕ[V] → ℕ[T] → 𝕊[T] → ℕ[ⓐV.T].
-/4 width=1/ qed.