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Proof step 22 from proof max_prime_divisor-nls-02 (previous step)

j < j0 * i, prime(j0), prime(j), 2 ≤ j * j0 * i, j < j0, 2 ≤ j0 * i, j + 1 < j0 * i, 0 < j, 0 < j0, 1 < j0, 2 < j0 * i, 0 ≤ i, 1 < i, 0 < i, ∀ j1. j < j1 ∧ j1 < j * j0 * i ∧ prime(j1) → ¬ j1 | j * j0 * i, ∀ j1. j0 < j1 ∧ j1 < j0 * i ∧ prime(j1) → ¬ j1 | j0 * i ⊦ prime(j * j0 * i)

User applied rule all left

And closed the goal!

Rule argument

pos: left 15 terms: j0 abort: F discard: T computed: T

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j;%ls-same-01: ⊦ 0 < i → (i < i * j ↔ 1 < j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%le-one: ⊦ 1 < j → (i * j ≤ 1 ↔ i ≤ 0); from specification int-mult%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: j0