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Step * 1 of Lemma funinv_wf2


1. n : ℕ
2. f : {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
3. f = f ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
⊢ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)}  ⊆r {f:ℕn ⟶ ℕn| Surj(ℕn;ℕn;f)} 
BY
{ (SubtypeReasoning THEN Auto THEN BLemma `injection-is-surjection` THEN Auto) }

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Latex:

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Latex:

1.  n  :  \mBbbN{}
2.  f  :  \{f:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Inj(\mBbbN{}n;\mBbbN{}n;f)\} 
3.  f  =  f
\mvdash{}  \{f:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Inj(\mBbbN{}n;\mBbbN{}n;f)\}    \msubseteq{}r  \{f:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Surj(\mBbbN{}n;\mBbbN{}n;f)\} 


By

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Latex:
(SubtypeReasoning  THEN  Auto  THEN  BLemma  `injection-is-surjection`  THEN  Auto)

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