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Proof step 29 from proof prime-def-prime (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 30:
i0 * i1 = i, 1 < i0, i0 < i0 * i1, 0 < i, 1 < i, i1 ≤ i0, prime(i1) ∧ i1 * i1 ≤ i → ¬ i1 | i, ∀ j. prime(j) ∧ j * j ≤ i → ¬ j | i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 ∧ 1 < i0 ∧ (∀ j. prime(j) ∧ j * j ≤ i0 → ¬ j | i0) → prime(i0) ⊦

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ 0 < j → (j < 2 ↔ j = 1); (s)