| | Some definitions of interest. |
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| 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 |
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| 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 |
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| iff | Def P   Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
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| l_disjoint | Def l_disjoint(T;l1;l2) == x:T.  ((x l1) & (x l2)) |
| | | Thm* T:Type, l,l':T List. l_disjoint(T;l;l') Prop |
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| no_repeats | Def no_repeats(T;l) == i,j: . i < ||l|| j < ||l|| i = j l[i] = l[j] T |
| | | Thm* T:Type, l:T List. no_repeats(T;l) Prop |
