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Proof step 5 from proof middle-coef-largest-01 (previous step)

0 < i, 0 ≤ j, j < i, binom_coef(2 * i, i) < binom_coef(2 * i, j), ∀ i0, j0. i→n(i0 - j0) < i→n(i - j) → binom_coef(2 * i0, i0) < binom_coef(2 * i0, j0) ∧ j0 < i0 ∧ 0 ≤ j0 ∧ 0 < i0 → false ⊦ binom_coef(2 * i, i) < binom_coef(2 * i, j + 1) ∧ j + 1 < i ∧ 0 ≤ j + 1 ∧ 0 < i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
0 < i, 0 ≤ j, j < i, binom_coef(2 * i, i) < binom_coef(2 * i, j), ∀ i0, j0. i→n(i0 - j0) < i→n(i - j) → binom_coef(2 * i0, i0) < binom_coef(2 * i0, j0) ∧ j0 < i0 ∧ 0 ≤ j0 ∧ 0 < i0 → false ⊦ binom_coef(2 * i, i) < binom_coef(2 * i, j + 1) ∧ j + 1 < i

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs