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[helm.git] / helm / software / matita / tests / ng_coercion_and_hints.ma

diff --git a/helm/software/matita/tests/ng_coercion_and_hints.ma b/helm/software/matita/tests/ng_coercion_and_hints.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "ng_pts.ma".
+ndefinition hint_declaration_Type0  ≝  λA:Type[0] .λa,b:A.a.
+ndefinition hint_declaration_Type1  ≝  λA:Type[1].λa,b:A.a.
+ndefinition hint_declaration_Type2  ≝  λa,b:Type[1].a.
+ndefinition hint_declaration_CProp0 ≝  λA:CProp[0].λa,b:A.a.
+ndefinition hint_declaration_CProp1 ≝  λA:CProp[1].λa,b:A.a.
+ndefinition hint_declaration_CProp2 ≝  λa,b:CProp[1].a.
+  
+notation > "≔ (list0 (ident x : T )sep ,) ⊢ term 19 Px ≡ term 19 Py"
+  with precedence 90
+  for @{ ${ fold right @{'hint_decl $Px $Py} rec acc @{ ∀${ident x}:$T.$acc } } }.      
+
+interpretation "hint_decl_Type2"  'hint_decl a b = (hint_declaration_Type2 a b).
+interpretation "hint_decl_CProp2" 'hint_decl a b = (hint_declaration_CProp2 a b).
+interpretation "hint_decl_Type1"  'hint_decl a b = (hint_declaration_Type1 ? a b).
+interpretation "hint_decl_CProp1" 'hint_decl a b = (hint_declaration_CProp1 ? a b).
+interpretation "hint_decl_CProp0" 'hint_decl a b = (hint_declaration_CProp0 ? a b).
+interpretation "hint_decl_Type0"  'hint_decl a b = (hint_declaration_Type0 ? a b).
+
+naxiom A : Type[0].
+naxiom B : Type[0].
+
+ndefinition C ≝ B.
+ndefinition D ≝ A.
+
+naxiom f : B → A.
+
+ncoercion pippo : ∀a:B. A ≝ f on _a : B to A.
+
+alias symbol "hint_decl" = "hint_decl_Type1".
+unification hint 0 ≔ ⊢ C ≡ B.
+unification hint 0 ≔ ⊢ A ≡ D.
+
+naxiom pippo : D → Prop.
+
+nlemma foo : ∀c:C. pippo c. 
+
+