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Step * of Lemma count-combinations

∀n,m:ℕ.  Combination(n;ℕm) ~ ℕC(n;m)
BY
{ TACTIC:(InductionOnNat THEN Auto) }

1
1. m : ℕ
⊢ Combination(0;ℕm) ~ ℕC(0;m)

2
1. n : ℤ
2. [%1] : 0 < n
3. ∀m:ℕ. Combination(n - 1;ℕm) ~ ℕC(n - 1;m)
4. m : ℕ
⊢ Combination(n;ℕm) ~ ℕC(n;m)

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Latex:

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Latex:
\mforall{}n,m:\mBbbN{}.    Combination(n;\mBbbN{}m)  \msim{}  \mBbbN{}C(n;m)


By

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Latex:
TACTIC:(InductionOnNat  THEN  Auto)

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