helm/software/matita/nlibrary/logic/destruct_bb.ma

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  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "logic/equality.ma".
  16
  17 (* nlemma prova : ∀T:Type[0].∀a,b:T.∀e:a = b.
  18                ∀P:∀x,y:T.x=y→Prop.P a a (refl T a) → P a b e.
  19 #T;#a;#b;#e;#P;#H;
  20 nrewrite < e;*)
  21
  22 ninductive I1 : Type[0] ≝
  23 | k1 : I1.
  24
  25 ninductive I2 : I1 → Type[0] ≝
  26 | k2 : ∀x.I2 x.
  27
  28 ninductive I3 : ∀x:I1.I2 x → Type[0] ≝
  29 | k3 : ∀x,y.I3 x y.
  30
  31 ninductive I4 : ∀x,y.I3 x y → Type[0] ≝
  32 | k4 : ∀x,y.∀z:I3 x y.I4 x y z.
  33
  34 (*alias id "eq" = "cic:/matita/ng/logic/equality/eq.ind(1,0,2)".
  35 alias id "refl" = "cic:/matita/ng/logic/equality/eq.con(0,1,2)".*)
  36
  37 ninductive II : Type[0] ≝
  38 | kII1 : ∀x,y,z.∀w:I4 x y z.II
  39 | kII2 : ∀x,y,z.∀w:I4 x y z.II.
  40
  41 (* nlemma foo : ∀a,b,c,d,e,f,g,h. kII1 a b c d = kII2 e f g h → True.
  42 #a;#b;#c;#d;#e;#f;#g;#h;#H;
  43 ndiscriminate H;
  44 nqed. *)
  45
  46 nlemma faof : ∀a,b,c,d,e,f,g,h.∀Heq:kII1 a b c d = kII1 e f g h.
  47               ∀P:(∀a,b,c,d.kII1 a b c d = kII1 e f g h → Prop).
  48               P e f g h (refl ??) → P a b c d Heq.
  49 #a;#b;#c;#d;#e;#f;#g;#h;#Heq;#P;#HP;
  50 ndestruct;
  51 napply HP;
  52 nqed.