File: Tescik.v

package info (click to toggle)
coq 8.0pl2-2
  • links: PTS
  • area: main
  • in suites: sarge
  • size: 14,228 kB
  • ctags: 17,685
  • sloc: ml: 97,070; makefile: 1,255; sh: 738; lisp: 456; awk: 15
file content (30 lines) | stat: -rw-r--r-- 469 bytes parent folder | download | duplicates (2) 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
 

Module Type ELEM.
  Parameter A:Set.
  Parameter x:A.
End ELEM.

Module Nat.
    Definition A:=nat.
    Definition x:=O.
End Nat. 

Module List[X:ELEM].
  Inductive list : Set := nil : list 
		       | cons : X.A -> list -> list.
 
  Definition head := 
     [l:list]Cases l of 
	  nil => X.x 
	| (cons x _) => x
     end.

  Definition singl := [x:X.A] (cons x nil).
  
  Lemma head_singl : (x:X.A)(head (singl x))=x.
  Auto.
  Qed.

End List.

Module N:=(List Nat).