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Proof step 5 from proof middle-coef-not-one-01 (previous step)

1 < i ∧ 0 ≤ 1 → ¬ binom_coef(2 * i, i) < binom_coef(2 * i, 1), binom_coef(2 * i, i) < 2, 0 < i ⊦ i = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
binom_coef(2 * i, i) < 2, binom_coef(2 * i, 1) ≤ binom_coef(2 * i, i), 1 < i, 0 < i, binom_coef(2 * i, 1) < 2 ⊦ i = 1

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1