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Proof step 9 from proof prime-def-mod (previous step)

j % i = 0, 0 < j, 0 < i, 1 < i, i * i ≤ j, 2 ≤ j, 0 ≤ j, i < j → ¬ i | j, ∀ i. 1 < i ∧ i < j → ¬ i | j ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 10:
j % i = 0, 1 < i, 0 < i, 0 < j, 0 ≤ j, 2 ≤ j, i * i ≤ j, i < j → ¬ i | j, ∀ i. 1 < i ∧ i < j → ¬ i | j ⊦ i = 1

Rule argument

fma: i = 1

Additional information

Used simplifier rules: ⊦ i % 1 = 0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 1 ≤ i ↔ 0 < i; (s) Used formulas: i = 1