| Some definitions of interest. |
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eqfun_p | Def IsEqFun(T;eq) == x,y:T. (x eq y) x = y |
| | Thm* T:Type, eq:(TT). IsEqFun(T;eq) Prop |
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assert | Def b == if b True else False fi |
| | Thm* b:. 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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least | Def least i:. p(i) == if p(0) 0 else (least i:. p(i+1))+1 fi (recursive) |
| | Thm* k:, p:{p:(k)| i:k. p(i) }. (least i:. p(i)) k |
| | Thm* p:{p:()| i:. p(i) }. (least i:. p(i)) |
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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 |