| | Who Cites habs num? |
|
| habs_num | Def abs_num ==  n: . @m:. (n = rep_num(m)  ) |
| | | Thm* abs_num (hind   hnum) |
|
| hrep_num | Def rep_num == n:. ncompose(suc_rep;n;zero_rep) |
| | | Thm* rep_num (hnum hind) |
|
| hzero_rep | Def zero_rep == @x:. ( y:.  x = suc_rep(y) ) |
| | | Thm* zero_rep hind |
|
| hsuc_rep | Def suc_rep == x:. (@f:. (one_one(;;f) & onto(;;f)))(x) |
| | | Thm* suc_rep (hind hind) |
|
| nat | Def == {i: | 0 i } |
| | | Thm* Type |
| | | Thm* S |
|
| choose | Def @x:T. P(x) == InjCase(lem({x:T| P(x) }); x. x, arb(T)) |
| | | Thm* T:S, P:(TType). (@x:T. P(x)) T |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
|
| ncompose | Def ncompose(f;n;x) == if n= 0 then x else f(ncompose(f;n-1;x)) fi (recursive) |
| | | Thm* 'a:Type, n:, x:'a, f:('a'a). ncompose(f;n;x) 'a |
|
| le | Def AB == B<A |
| | | Thm* i,j:. (ij) Prop |
|
| arb | Def arb(T) == InjCase(lem(T); x. x, "uu") |
| | | Thm* T:S. arb(T) T |
|
| not | Def A == A   False |
| | | Thm* A:Prop. (A) Prop |
|
| onto | Def onto('a;'b;f) == y:'b.  x:'a. y = f(x) |
| | | Thm* 'a,'b:Type, f:('a'b). onto('a;'b;f) Prop |
|
| one_one | Def one_one('a;'b;f) == x,y:'a. f(x) = f(y) 'b x = y |
| | | Thm* 'a,'b:Type, f:('a'b). one_one('a;'b;f) Prop |
|
| eq_int | Def i=j == if i=j true ; false fi |
| | | Thm* i,j:. (i=j)  |
|
| bif | Def bif(b; bx.x(bx); by.y(by)) == if b x(*) else y(x.x) fi |
| | | Thm* A:Type, b:, x:(bA), y:((b)A). bif(b; bx.x(bx); by.y(by)) A |
