...

[helm.git] / helm / software / matita / nlibrary / logic / destruct_bb.ma

diff --git a/helm/software/matita/nlibrary/logic/destruct_bb.ma b/helm/software/matita/nlibrary/logic/destruct_bb.ma
index d3d2aadc3a7fbe3270574403ed7d18c9772eb44c..308f8bebeb91ed3b554cca708bb4e6fbd0eb1124 100644 (file)
--- a/helm/software/matita/nlibrary/logic/destruct_bb.ma
+++ b/helm/software/matita/nlibrary/logic/destruct_bb.ma
@@ -11,72 +11,49 @@
 (*        v         GNU General Public License Version 2                  *)
 (*                                                                        *)
 (**************************************************************************)
-(*
-include "nat/nat.ma".
-include "list/list.ma".
 
-inductive index_list (T: nat → Type): ∀m,n:nat.Type ≝
-| il_s : ∀n.T n → index_list T n n
-| il_c : ∀m,n. T m → index_list T (S m) n → index_list T m n.
-
-lemma down_il : ∀T:nat → Type.∀m,n.∀l: index_list T m n.∀f:(∀p. T (S p) → T p).
-                ∀m',n'.S m' = m → S n' = n → index_list T m' n'.
-intros 5;elim i
-[destruct;apply il_s;apply f;assumption
-|apply il_c
- [apply f;rewrite > H;assumption
- |apply f1
-  [rewrite > H;reflexivity
-  |assumption]]]
-qed.
+include "logic/equality.ma".
 
-definition r1 : ∀T0,T1,a0,b0,e0.T1 a0 → T1 b0 ≝
-  λT0:Type.λT1:T0 → Type.
-  λa0,b0:T0.
-  λe0:a0 = b0.
-  λso:T1 a0.
-  eq_rect' ?? (λy,p.T1 y) so ? e0.
-  *)
+ninductive unit: Type[0] ≝ k: unit.
 
-include "logic/equality.ma".
-  
-ndefinition R1 ≝ eq_rect_Type0.
+ninductive bool: unit → Type[0] ≝ true : bool k | false : bool k.
 
-ndefinition R2 :
-  ∀T0:Type[0].
-  ∀a0:T0.
-  ∀T1:∀x0:T0. a0=x0 → Type[0].
-  ∀a1:T1 a0 (refl ? a0).
-  ∀T2:∀x0:T0. ∀p0:a0=x0. ∀x1:T1 x0 p0. R1 ??? a1 ? p0 = x1 → Type[0].
-  ∀b0:T0.
-  ∀e0:a0 = b0.
-  ∀b1: T1 b0 e0.
-  ∀e1:R1 ??? a1 ? e0 = b1.
-  ∀so:T2 a0 (refl ? a0) a1 (refl ? a1).T2 b0 e0 b1 e1.
-#T0;#a0;#T1;#a1;#T2;#b0;#e0;#b1;#e1;#H;
-napply (eq_rect_Type0 ????? e1);
-napply (R1 ?? ? ?? e0);
-napply H;
+nlemma foo: true = false → False. #H; ndestruct;
 nqed.
 
-ndefinition R3 :
-  ∀T0:Type[0].
-  ∀a0:T0.
-  ∀T1:∀x0:T0. a0=x0 → Type[0].
-  ∀a1:T1 a0 (refl ? a0).
-  ∀T2:∀x0:T0. ∀p0:a0=x0. ∀x1:T1 x0 p0. R1 ??? a1 ? p0 = x1 → Type[0].
-  ∀a2:T2 a0 (refl ? a0) a1 (refl ? a1).
-  ∀T3:∀x0:T0. ∀p0:a0=x0. ∀x1:T1 x0 p0.∀p1:R1 ??? a1 ? p0 = x1.
-      ∀x2:T2 x0 p0 x1 p1.R2 ???? T2 x0 p0 ? p1 a2 = x2 → Type[0].
-  ∀b0:T0.
-  ∀e0:a0 = b0.
-  ∀b1: T1 b0 e0.
-  ∀e1:R1 ??? a1 ? e0 = b1.
-  ∀b2: T2 b0 e0 b1 e1.
-  ∀e2:R2 ???? T2 b0 e0 ? e1 a2 = b2.
-  ∀so:T3 a0 (refl ? a0) a1 (refl ? a1) a2 (refl ? a2).T3 b0 e0 b1 e1 b2 e2.
-#T0;#a0;#T1;#a1;#T2;#a2;#T3;#b0;#e0;#b1;#e1;#b2;#e2;#H;
-napply (eq_rect_Type0 ????? e2);
-napply (R2 ?? ? ??? e0 ? e1);
-napply H;
+(* nlemma prova : ∀T:Type[0].∀a,b:T.∀e:a = b.
+               ∀P:∀x,y:T.x=y→Prop.P a a (refl T a) → P a b e.
+#T;#a;#b;#e;#P;#H;
+nrewrite < e;*)
+
+ninductive I1 : Type[0] ≝
+| k1 : I1.
+
+ninductive I2 : I1 → Type[0] ≝
+| k2 : ∀x.I2 x.
+
+ninductive I3 : ∀x:I1.I2 x → Type[0] ≝
+| k3 : ∀x,y.I3 x y.
+
+ninductive I4 : ∀x,y.I3 x y → Type[0] ≝
+| k4 : ∀x,y.∀z:I3 x y.I4 x y z.
+
+(*alias id "eq" = "cic:/matita/ng/logic/equality/eq.ind(1,0,2)".
+alias id "refl" = "cic:/matita/ng/logic/equality/eq.con(0,1,2)".*)
+
+ninductive II : Type[0] ≝
+| kII1 : ∀x,y,z.∀w:I4 x y z.II
+| kII2 : ∀x,y,z.∀w:I4 x y z.II.
+
+(* nlemma foo : ∀a,b,c,d,e,f,g,h. kII1 a b c d = kII2 e f g h → True.
+#a;#b;#c;#d;#e;#f;#g;#h;#H;
+ndiscriminate H;
+nqed. *)
+
+nlemma faof : ∀a,b,c,d,e,f,g,h.∀Heq:kII1 a b c d = kII1 e f g h.
+              ∀P:(∀a,b,c,d.kII1 a b c d = kII1 e f g h → Prop).
+              P e f g h (refl ??) → P a b c d Heq.
+#a;#b;#c;#d;#e;#f;#g;#h;#Heq;#P;#HP;
+ndestruct;
+napply HP;
 nqed.
\ No newline at end of file