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Step * 1 of Lemma biject-iff-inverse


1. [A] : Type
2. [B] : Type
3. f : A ⟶ B@i
4. ∃g:B ⟶ A. InvFuns(A;B;f;g)@i
⊢ Bij(A;B;f)
BY
{ (D (-1) THEN InstLemma `fun_with_inv_is_bij` [⌜A⌝;⌜B⌝;⌜f⌝;⌜g⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  [A]  :  Type
2.  [B]  :  Type
3.  f  :  A  {}\mrightarrow{}  B@i
4.  \mexists{}g:B  {}\mrightarrow{}  A.  InvFuns(A;B;f;g)@i
\mvdash{}  Bij(A;B;f)


By

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Latex:
(D  (-1)  THEN  InstLemma  `fun\_with\_inv\_is\_bij`  [\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}g\mkleeneclose{}]\mcdot{}  THEN  Auto)

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