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Step * of Lemma mk_lambdas_fun-eta

∀[F:Top]. ∀[m:ℕ].  (mk_lambdas_fun(F;m) ~ mk_lambdas_fun(λg.(F (λx.(g x)));m))
BY
{ ((UnivCD THENA Auto)
   THEN RepUR ``mk_lambdas_fun`` 0
   THEN (InstLemma `mk_lambdas-fun-eta` [⌜F⌝;⌜λx.x⌝;⌜m⌝;⌜0⌝]⋅ THENA Auto)
   THEN RepUR ``mk_applies`` (-1)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[F:Top].  \mforall{}[m:\mBbbN{}].    (mk\_lambdas\_fun(F;m)  \msim{}  mk\_lambdas\_fun(\mlambda{}g.(F  (\mlambda{}x.(g  x)));m))


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  RepUR  ``mk\_lambdas\_fun``  0
  THEN  (InstLemma  `mk\_lambdas-fun-eta`  [\mkleeneopen{}F\mkleeneclose{};\mkleeneopen{}\mlambda{}x.x\mkleeneclose{};\mkleeneopen{}m\mkleeneclose{};\mkleeneopen{}0\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  RepUR  ``mk\_applies``  (-1)
  THEN  Auto)

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