| Some definitions of interest. |
|
assert | Def b == if b True else False fi |
| | Thm* b:. b Prop |
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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 |
| | Thm* A,B,C:Type, f:(B inj C), g:(A inj B). f o g A inj C |
| | Thm* f:(B onto C), g:(A onto B). f o g A onto C |
|
iff | Def P Q == (P Q) & (P Q) |
| | Thm* A,B:Prop. (A B) Prop |
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int_seg | Def {i..j} == {k:| i k < j } |
| | Thm* m,n:. {m..n} Type |
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is_discrete | Def A Discrete == x,y:A. Dec(x = y) |
| | Thm* A:Type. (A Discrete) Prop |
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nat | Def == {i:| 0i } |
| | Thm* Type |
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surjection_type | Def A onto B == {f:(AB)| Surj(A; B; f) } |
| | Thm* A,B:Type. A onto B Type |
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surject | Def Surj(A; B; f) == b:B. a:A. f(a) = b |
| | Thm* A,B:Type, f:(AB). Surj(A; B; f) Prop |