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Proof step 23 from proof max_prime_divisor-nls-02 (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 14 terms: j0 abort: F discard: T computed: T

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j;% ⊦ 0 < i → (i < i * j ↔ 1 < j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ 1 < j → (i * j ≤ 1 ↔ i ≤ 0); (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: j0