| | Some definitions of interest. |
|
| fpf-join | Def f  g == <1of(f) @ filter( a.  a  dom(f);1of(g)),a.f(a)?g(a)> |
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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 |
|
| deq | Def EqDecider(T) == eq:T  T  x,y:T. x = y    (eq(x,y)) |
| | | Thm* T:Type. EqDecider(T) Type |
|
| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
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| fpf-dom | Def x dom(f) == deq-member(eq;x;1of(f)) |
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| deq-member | Def deq-member(eq;x;L) == reduce(a,b. eqof(eq)(a,x)  b;false;L) |
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| filter | Def filter(P;l) == reduce(a,v. if P(a) [a / v] else v fi;nil;l) |
| | | Thm* T:Type, P:(T), l:T List. filter(P;l) T List |
|
| fpf | Def a:A fp-> B(a) == d:A Lista:{a:A| (a d) }B(a) |
| | | Thm* A:Type, B:(AType). a:A fp-> B(a) Type |
|
| iff | Def P Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
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| l_member | Def (x l) ==  i: . i<||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
|
| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
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| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
