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Proof step 9 from proof coef-le-2pot (previous step)

binom_coef(2 * j + 1, j) = binom_coef(2 * j + 1, j + 1), 2 ^ (2 * j) * 2 = Σ countFun(0, 2 * j + 1, λ j0. binom_coef(2 * j + 1, j0)), 2 ^ (2 * j) < binom_coef(2 * j + 1, j), 0 < j, 0 ≤ j ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
binom_coef(2 * j + 1, j) = binom_coef(2 * j + 1, j + 1), 2 ^ (2 * j) * 2 = Σ countFun(0, 2 * j + 1, λ j0. binom_coef(2 * j + 1, j0)), 2 ^ (2 * j) < binom_coef(2 * j + 1, j + 1), 0 < j, 0 ≤ j ⊦

Proof step 9 from proof coef-le-2pot (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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