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Proof step 27 from proof prime-def-prime (previous step)

1 < i, 0 < i, i1 ≤ i0, ∀ 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 all left

And obtained the following new goals

Proof step 28:
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) ⊦ 2 ≤ i ∧ (1 < i0 ∧ i0 < i0 * i1 → i0 * i1 ≠ i)

Rule argument

pos: left 4 terms: i1 abort: F discard: F computed: T

Additional information

Used terms: i1