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Proof step 13 from proof coef-le-2pot (previous step)

2 * 2 ^ (2 * j) < binom_coef(2 * j + 1, j) + binom_coef(2 * j + 1, j + 1), 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 ⊦

User applied rule insert equation

And obtained the following new goals

Proof step 14:
Σ countFun(0, 2 * j + 1, λ j0. binom_coef(2 * j + 1, j0)) < binom_coef(2 * j + 1, j) + binom_coef(2 * j + 1, j + 1), 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 ⊦

Rule argument

pos: left 3 flags:

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult