| | Some definitions of interest. |
|
| paren | Def paren(T;s) == s = nil  (T+T) List  ( t:T, s':(T+T) List. s = ([inl(t)] @ s' @ [inr(t)]) & paren(T;s')) (s',s'':(T+T) List. ||s'|| < ||s|| & ||s''|| < ||s|| & s = (s' @ s'') & paren(T;s') & paren(T;s'')) (recursive) |
| | | Thm*  T:Type, s:(T+T) List. paren(T;s) Prop |
|
| append | Def as @ bs == Case of as; nil  bs ; a.as' [a / (as' @ bs)] (recursive) |
| | | Thm* T:Type, as,bs:T List. (as @ bs) T List |
|
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l||  |
| | | Thm* ||nil|| |
|
| nat | Def  == {i:| 0 i } |
| | | Thm* Type |
