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Proof step 4 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 ⊦

User applied rule apply induction

And obtained the following new goals

Proof step 5:
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

Rule argument

subst: [i0, j0] → [i, j + 1]

Additional information

Used simplifier rules: labs: ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j); from specification intnat%abssub-02: ⊦ j < i → abs(i - j) = i - j; from specification int-abs%abssub-01: ⊦ j < i → abs(i - j + 1) = i - j + 1; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%irreflexivity: ⊦ ¬ i < i; from specification oelem[intlista] Used terms: i, j + 1