freescale porting, work in progress

[helm.git] / helm / software / matita / contribs / ng_assembly / freescale / theory.ma

diff --git a/helm/software/matita/contribs/ng_assembly/freescale/theory.ma b/helm/software/matita/contribs/ng_assembly/freescale/theory.ma
index 3e108e7bebb4620ae15957f7cd2979aabf134516..a9e6287a8a074741fd7a3f140f01b3b7120cb004 100644 (file)
--- a/helm/software/matita/contribs/ng_assembly/freescale/theory.ma
+++ b/helm/software/matita/contribs/ng_assembly/freescale/theory.ma
@@ -31,32 +31,8 @@ include "freescale/pts.ma".
 ninductive True: Prop ≝
  I : True.
 
-(*ndefinition True_ind_xx : ΠP:Prop.P → True → P ≝
-λP:Prop.λp:P.λH:True.
- match H with [ I ⇒ p ].
-
-ndefinition True_rec_xx : ΠP:Set.P → True → P ≝
-λP:Set.λp:P.λH:True.
- match H with [ I ⇒ p ].
-
-ndefinition True_rect_xx : ΠP:Type.P → True → P ≝
-λP:Type.λp:P.λH:True.
- match H with [ I ⇒ p ].*)
-
 ninductive False: Prop ≝.
 
-(*ndefinition False_ind_xx : ΠP:Prop.False → P ≝
-λP:Prop.λH:False.
- match H in False return λH1:False.P with [].
-
-ndefinition False_rec_xx : ΠP:Set.False → P ≝
-λP:Set.λH:False.
- match H in False return λH1:False.P with [].
-
-ndefinition False_rect_xx : ΠP:Type.False → P ≝
-λP:Type.λH:False.
- match H in False return λH1:False.P with [].*)
-
 ndefinition Not: Prop → Prop ≝
 λA.(A → False).
 
@@ -79,30 +55,19 @@ nqed.
 ninductive And (A,B:Prop) : Prop ≝
  conj : A → B → (And A B).
 
-(*ndefinition And_ind_xx : ΠA,B:Prop.ΠP:Prop.(A → B → P) → And A B → P ≝
-λA,B:Prop.λP:Prop.λf:A → B → P.λH:And A B.
- match H with [conj H1 H2 ⇒ f H1 H2 ].
-
-ndefinition And_rec_xx : ΠA,B:Prop.ΠP:Set.(A → B → P) → And A B → P ≝
-λA,B:Prop.λP:Set.λf:A → B → P.λH:And A B.
- match H with [conj H1 H2 ⇒ f H1 H2 ].
-
-ndefinition And_rect_xx : ΠA,B:Prop.ΠP:Type.(A → B → P) → And A B → P ≝
-λA,B:Prop.λP:Type.λf:A → B → P.λH:And A B.
- match H with [conj H1 H2 ⇒ f H1 H2 ].*)
-
 interpretation "logical and" 'and x y = (And x y).
 
 nlemma proj1: ∀A,B:Prop.A ∧ B → A.
  #A; #B; #H;
- napply (And_ind A B ?? H);
+ (* \ldots al posto di ??? *)
+ napply (And_ind A B … H);
  #H1; #H2;
  napply H1.
 nqed.
 
 nlemma proj2: ∀A,B:Prop.A ∧ B → B.
  #A; #B; #H;
- napply (And_ind A B ?? H);
+ napply (And_ind A B … H);
  #H1; #H2;
  napply H2.
 nqed.
@@ -111,10 +76,6 @@ ninductive Or (A,B:Prop) : Prop ≝
   or_introl : A → (Or A B)
 | or_intror : B → (Or A B).
 
-(*ndefinition Or_ind_xx : ΠA,B:Prop.ΠP:Prop.(A → P) → (B → P) → Or A B → P ≝
-λA,B:Prop.λP:Prop.λf1:A → P.λf2:B → P.λH:Or A B.
- match H with [ or_introl H1 ⇒ f1 H1 | or_intror H1 ⇒ f2 H1 ].*)
-
 interpretation "logical or" 'or x y = (Or x y).
 
 ndefinition decidable : Prop → Prop ≝ λA:Prop.A ∨ ¬A.
@@ -122,21 +83,13 @@ ndefinition decidable : Prop → Prop ≝ λA:Prop.A ∨ ¬A.
 ninductive ex (A:Type) (Q:A → Prop) : Prop ≝
  ex_intro: ∀x:A.Q x → ex A Q.
 
-(*ndefinition ex_ind_xx : ΠA:Type.ΠQ:A → Prop.ΠP:Prop.(Πa:A.Q a → P) → ex A Q → P ≝
-λA:Type.λQ:A → Prop.λP:Prop.λf:(Πa:A.Q a → P).λH:ex A Q.
- match H with [ ex_intro H1 H2 ⇒ f H1 H2 ].*)
-
 interpretation "exists" 'exists x = (ex ? x).
 
 ninductive ex2 (A:Type) (Q,R:A → Prop) : Prop ≝
  ex_intro2: ∀x:A.Q x → R x → ex2 A Q R.
 
-(*ndefinition ex2_ind_xx : ΠA:Type.ΠQ,R:A → Prop.ΠP:Prop.(Πa:A.Q a → R a → P) → ex2 A Q R → P ≝
-λA:Type.λQ,R:A → Prop.λP:Prop.λf:(Πa:A.Q a → R a → P).λH:ex2 A Q R.
- match H with [ ex_intro2 H1 H2 H3 ⇒ f H1 H2 H3 ].*)
-
 ndefinition iff ≝
-λA,B.(A -> B) ∧ (B -> A).
+λA,B.(A → B) ∧ (B → A).
 
 (* higher_order_defs/relations *)
 
@@ -169,18 +122,6 @@ ndefinition antisymmetric : ∀A:Type.∀R:relation A.Prop ≝
 ninductive eq (A:Type) (x:A) : A → Prop ≝
  refl_eq : eq A x x.
 
-(*ndefinition eq_ind_xx : ΠA:Type.Πx:A.ΠP:A → Prop.P x → Πa:A.eq A x a → P a ≝
-λA:Type.λx:A.λP:A → Prop.λp:P x.λa:A.λH:eq A x a.
- match H with [refl_eq ⇒ p ].
-
-ndefinition eq_rec_xx : ΠA:Type.Πx:A.ΠP:A → Set.P x → Πa:A.eq A x a → P a ≝
-λA:Type.λx:A.λP:A → Set.λp:P x.λa:A.λH:eq A x a.
- match H with [refl_eq ⇒ p ].
-
-ndefinition eq_rect_xx : ΠA:Type.Πx:A.ΠP:A → Type.P x → Πa:A.eq A x a → P a ≝
-λA:Type.λx:A.λP:A → Type.λp:P x.λa:A.λH:eq A x a.
- match H with [refl_eq ⇒ p ].*)
-
 interpretation "leibnitz's equality" 'eq t x y = (eq t x y).
 
 interpretation "leibnitz's non-equality" 'neq t x y = (Not (eq t x y)).
@@ -190,14 +131,13 @@ nlemma symmetric_eq: ∀A:Type. symmetric A (eq A).
  nnormalize;
  #x; #y; #H;
  nrewrite < H;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma eq_elim_r: ∀A:Type.∀x:A.∀P:A → Prop.P x → ∀y:A.y=x → P y.
  #A; #x; #P; #H; #y; #H1;
- nletin H2 ≝ (symmetric_eq ??? H1);
- nrewrite < H2;
- nassumption.
+ nrewrite < (symmetric_eq … H1);
+ napply H.
 nqed.
 
 ndefinition relationT : Type → Type → Type ≝
@@ -213,12 +153,12 @@ ndefinition associative : ∀A:Type.∀R:relationT A A.Prop ≝
 
 ninductive list (A:Type) : Type ≝
   nil: list A
-| cons: A -> list A -> list A.
+| cons: A → list A → list A.
 
 nlet rec append A (l1: list A) l2 on l1 ≝
  match l1 with
-  [ nil => l2
-  | (cons hd tl) => cons A hd (append A tl l2) ].
+  [ nil ⇒ l2
+  | (cons hd tl) ⇒ cons A hd (append A tl l2) ].
 
 notation "hvbox(hd break :: tl)"
   right associative with precedence 47
@@ -241,7 +181,7 @@ nlemma list_destruct_1 : ∀T.∀x1,x2:T.∀y1,y2:list T.cons T x1 y1 = cons T x
  nchange with (match cons T x2 y2 with [ nil ⇒ False | cons a _ ⇒ x1 = a ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma list_destruct_2 : ∀T.∀x1,x2:T.∀y1,y2:list T.cons T x1 y1 = cons T x2 y2 → y1 = y2.
@@ -249,7 +189,7 @@ nlemma list_destruct_2 : ∀T.∀x1,x2:T.∀y1,y2:list T.cons T x1 y1 = cons T x
  nchange with (match cons T x2 y2 with [ nil ⇒ False | cons _ b ⇒ y1 = b ]);
  nrewrite < H;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma list_destruct_cons_nil : ∀T.∀x:T.∀y:list T.cons T x y = nil T → False.
@@ -270,35 +210,35 @@ nqed.
 
 nlemma append_nil : ∀T:Type.∀l:list T.(l@[]) = l.
  #T; #l;
- napply (list_ind T ??? l);
+ nelim l;
  nnormalize;
- ##[ ##1: napply (refl_eq ??)
+ ##[ ##1: napply refl_eq
  ##| ##2: #x; #y; #H;
           nrewrite > H;
-          napply (refl_eq ??)
+          napply refl_eq
  ##]
 nqed.
 
 nlemma associative_list : ∀T.associative (list T) (append T).
  #T; #x; #y; #z;
- napply (list_ind T ??? x);
+ nelim x;
  nnormalize;
- ##[ ##1: napply (refl_eq ??)
+ ##[ ##1: napply refl_eq
  ##| ##2: #a; #b; #H;
           nrewrite > H;
-          napply (refl_eq ??)
+          napply refl_eq
  ##]
 nqed.
 
 nlemma cons_append_commute : ∀T:Type.∀l1,l2:list T.∀a:T.a :: (l1 @ l2) = (a :: l1) @ l2.
  #T; #l1; #l2; #a;
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.
 
 nlemma append_cons_commute : ∀T:Type.∀a:T.∀l,l1:list T.l @ (a::l1) = (l@[a]) @ l1.
  #T; #a; #l; #l1;
  nrewrite > (associative_list T l [a] l1);
  nnormalize;
- napply (refl_eq ??).
+ napply refl_eq.
 nqed.