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Step * of Lemma fact-bound

∀n:ℕ. ((n)! ≤ n^n)
BY
{ ((InductionOnNat THEN Auto)
   THEN (RWO "exp_step fact_unroll_1" 0 THEN Auto)
   THEN (InstLemma `exp_preserves_le` [⌜n - 1⌝;⌜n - 1⌝;⌜n⌝]⋅ THEN Auto)
   THEN RWW "-2 -1" 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}n:\mBbbN{}.  ((n)!  \mleq{}  n\^{}n)


By

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Latex:
((InductionOnNat  THEN  Auto)
  THEN  (RWO  "exp\_step  fact\_unroll\_1"  0  THEN  Auto)
  THEN  (InstLemma  `exp\_preserves\_le`  [\mkleeneopen{}n  -  1\mkleeneclose{};\mkleeneopen{}n  -  1\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THEN  RWW  "-2  -1"  0
  THEN  Auto)

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