| | Some definitions of interest. |
|
| hall | Def all ==  p:'a   .   x:'a. (p(x)) |
| | | Thm* 'a:S. all  (('a hbool) hbool) |
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| hexists_unique | Def exists_unique == p:'a. b_exists_unique('a;x.p(x)) |
| | | Thm* 'a:S. exists_unique (('a hbool) hbool) |
|
| assert | Def  b == if b True else False fi |
| | | Thm* b:. b Prop |
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| ho | Def o == f:'a'b. g:'a'b. f o g |
| | | Thm* 'b,'c,'a:S. o (('b 'c) ('a 'b) 'a 'c) |
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| compose | Def (f o g)(x) == f(g(x)) |
| | | Thm* A,B,C:Type, f:(BC), g:(AB). f o g AC |
|
| hand | Def and == p:. q:. p  q |
| | | Thm* and (hbool hbool hbool) |
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| hequal | Def equal == x:'a. y:'a. x = y |
| | | Thm* 'a:S. equal ('a 'a hbool) |
|
| hfun | Def 'a 'b == 'a'b |
| | | Thm* 'a,'b:S. ('a 'b) S |
|
| hinl | Def inl == x:'a. inl(x) |
| | | Thm* 'a,'b:S. inl ('a hsum('a; 'b)) |
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| hinr | Def inr == x:'b. inr(x) |
| | | Thm* 'b,'a:S. inr ('b hsum('a; 'b)) |
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| hsum | Def hsum('a; 'b) == 'a+'b |
| | | Thm* 'a,'b:S. hsum('a; 'b) S |
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| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
