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Proof step 17 from proof prime-def-prime (previous step)

0 ≤ i1, 2 ≤ i0 * i1, 0 < i0, 2 < i0 * i1, 1 < i0, 1 < i1, 0 < i1, ∀ j. prime(j) ∧ j * j ≤ i0 * i1 → ¬ j | i0 * i1, ∀ i2. i→n(i2) < i→n(i0 * i1) → 0 < i2 ∧ 1 < i2 ∧ (∀ j. prime(j) ∧ j * j ≤ i2 → ¬ j | i2) → prime(i2) ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 18:
i0 < i1, 0 ≤ i1, 2 ≤ i0 * i1, 0 < i0, 2 < i0 * i1, 1 < i0, 1 < i1, 0 < i1, ∀ j. prime(j) ∧ j * j ≤ i0 * i1 → ¬ j | i0 * i1, ∀ i2. i→n(i2) < i→n(i0 * i1) → 0 < i2 ∧ 1 < i2 ∧ (∀ j. prime(j) ∧ j * j ≤ i2 → ¬ j | i2) → prime(i2) ⊦
Proof step 24:
0 ≤ i1, 2 ≤ i0 * i1, 0 < i0, 2 < i0 * i1, 1 < i0, 1 < i1, 0 < i1, ∀ j. prime(j) ∧ j * j ≤ i0 * i1 → ¬ j | i0 * i1, ∀ i2. i→n(i2) < i→n(i0 * i1) → 0 < i2 ∧ 1 < i2 ∧ (∀ j. prime(j) ∧ j * j ≤ i2 → ¬ j | i2) → prime(i2) ⊦ i0 < i1

Rule argument

fma: i0 < i1

Additional information

Used formulas: i0 < i1