closure property S4 added to abstract candidates of reducibility ...

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

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/trf.ma b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/trf.ma
index d0050452bcc14921b891ee0538bf40dd8ca77fc8..24b9e43f5527087d0fe112e32eea860f0a98238a 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/trf.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/trf.ma
@@ -17,7 +17,7 @@ include "Basic_2/grammar/term_simple.ma".
 (* CONTEXT-FREE REDUCIBLE AND IRREDUCIBLE TERMS *****************************)
 
 (* reducible terms *)
-inductive trf: term → Prop ≝
+inductive trf: predicate term ≝
 | trf_abst_sn: ∀V,T.   trf V → trf (𝕔{Abst} V. T)
 | trf_abst_dx: ∀V,T.   trf T → trf (𝕔{Abst} V. T)
 | trf_appl_sn: ∀V,T.   trf V → trf (𝕔{Appl} V. T)
@@ -32,8 +32,7 @@ interpretation
    'Reducible T = (trf T).
 
 (* irreducible terms *)
-definition tif: term → Prop ≝
-   λT. ℝ[T] → False.
+definition tif: predicate term ≝ λT. ℝ[T] → False.
 
 interpretation
    "context-free irreducibility (term)"
@@ -54,12 +53,12 @@ fact trf_inv_atom_aux: ∀I,T. ℝ[T] → T =  𝕒{I} → False.
 qed.
 
 lemma trf_inv_atom: ∀I. ℝ[𝕒{I}] → False.
-/2/ qed.
+/2 width=4/ qed-.
 
 fact trf_inv_abst_aux: ∀W,U,T. ℝ[T] → T =  𝕔{Abst} W. U → ℝ[W] ∨ ℝ[U].
 #W #U #T * -T
-[ #V #T #HV #H destruct -V T /2/
-| #V #T #HT #H destruct -V T /2/
+[ #V #T #HV #H destruct /2 width=1/
+| #V #T #HT #H destruct /2 width=1/
 | #V #T #_ #H destruct
 | #V #T #_ #H destruct
 | #V #T #H destruct
@@ -69,51 +68,51 @@ fact trf_inv_abst_aux: ∀W,U,T. ℝ[T] → T =  𝕔{Abst} W. U → ℝ[W] ∨
 qed.
 
 lemma trf_inv_abst: ∀V,T. ℝ[𝕔{Abst}V.T] → ℝ[V] ∨ ℝ[T].
-/2/ qed.
+/2 width=3/ qed-.
 
 fact trf_inv_appl_aux: ∀W,U,T. ℝ[T] → T =  𝕔{Appl} W. U →
                        ∨∨ ℝ[W] | ℝ[U] | (𝕊[U] → False).
 #W #U #T * -T
 [ #V #T #_ #H destruct
 | #V #T #_ #H destruct
-| #V #T #HV #H destruct -V T /2/
-| #V #T #HT #H destruct -V T /2/
+| #V #T #HV #H destruct /2 width=1/
+| #V #T #HT #H destruct /2 width=1/
 | #V #T #H destruct
 | #V #T #H destruct
-| #V #W0 #T #H destruct -V U
+| #V #W0 #T #H destruct
   @or3_intro2 #H elim (simple_inv_bind … H)
 ]
 qed.
 
 lemma trf_inv_appl: ∀W,U. ℝ[𝕔{Appl}W.U] → ∨∨ ℝ[W] | ℝ[U] | (𝕊[U] → False).
-/2/ qed.
+/2 width=3/ qed-.
 
 lemma tif_inv_abbr: ∀V,T. 𝕀[𝕔{Abbr}V.T] → False.
-/2/ qed.
+/2 width=1/ qed-.
 
 lemma tif_inv_abst: ∀V,T. 𝕀[𝕔{Abst}V.T] → 𝕀[V] ∧ 𝕀[T].
-/4/ qed.
+/4 width=1/ qed-.
 
 lemma tif_inv_appl: ∀V,T. 𝕀[𝕔{Appl}V.T] → ∧∧ 𝕀[V] & 𝕀[T] & 𝕊[T].
-#V #T #HVT @and3_intro /3/
-generalize in match HVT -HVT; elim T -T //
-* // * #U #T #_ #_ #H elim (H ?) -H /2/
-qed. 
+#V #T #HVT @and3_intro /3 width=1/
+generalize in match HVT; -HVT elim T -T //
+* // * #U #T #_ #_ #H elim (H ?) -H /2 width=1/
+qed-.
 
 lemma tif_inv_cast: ∀V,T. 𝕀[𝕔{Cast}V.T] → False.
-/2/ qed.
+/2 width=1/ qed-.
 
 (* Basic properties *********************************************************)
 
 lemma tif_atom: ∀I. 𝕀[𝕒{I}].
-/2/ qed.
+/2 width=4/ qed.
 
 lemma tif_abst: ∀V,T. 𝕀[V] →  𝕀[T] →  𝕀[𝕔 {Abst}V.T].
 #V #T #HV #HT #H
-elim (trf_inv_abst … H) -H /2/
+elim (trf_inv_abst … H) -H /2 width=1/
 qed.
 
 lemma tif_appl: ∀V,T. 𝕀[V] →  𝕀[T] →  𝕊[T] → 𝕀[𝕔{Appl}V.T].
 #V #T #HV #HT #S #H
-elim (trf_inv_appl … H) -H /2/
+elim (trf_inv_appl … H) -H /2 width=1/
 qed.