| Some definitions of interest. |
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eq_int | Def i= j == if i=j true ; false fi |
| | Thm* i,j: . (i= j) ![](FONT/bool.png) |
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injection_type | Def A inj B == {f:(A![](FONT/dash.png) B)| Inj(A; B; f) } |
| | Thm* A,B:Type. A inj B Type |
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inject | Def Inj(A; B; f) == a1,a2:A. f(a1) = f(a2) B ![](FONT/eq.png) a1 = a2 |
| | Thm* A,B:Type, f:(A![](FONT/dash.png) B). Inj(A; B; f) Prop |
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int_seg | Def {i..j } == {k: | i k < j } |
| | Thm* m,n: . {m..n } Type |
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inv_funs_2 | Def InvFuns(A;B;f;g) == ( x:A. g(f(x)) = x) & ( y:B. f(g(y)) = y) |
| | Thm* f:(A![](FONT/dash.png) B), g:(B![](FONT/dash.png) A). InvFuns(A;B;f;g) Prop |
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nat_plus | Def ![](FONT/nat.png) == {i: | 0<i } |
| | Thm* ![](FONT/nat.png) Type |
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not | Def A == A ![](FONT/eq.png) False |
| | Thm* A:Prop. ( A) Prop |