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Proof step 4 from proof middle-coef-larger-strongest (previous step)

0 ≤ 2 * i → (1 + 1) ^ (2 * i) = Σ countFun(0, 2 * i, λ j0. binom_coef(2 * i, j0) * 1 ^ j0 * 1 ^ (2 * i - j0)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%one: ⊦ 1 * i = i; from specification int-mult%one-01: ⊦ 1 ^ j = 1; from specification int-pot%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult