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Proof step 5 from proof pot-mod-zero (previous step)

0 ≤ j0 ∧ 0 ≤ j1 - j0, j ^ j1 = j ^ j0 * j ^ (j1 - j0), j0 ≤ j1, 0 < j, 0 ≤ j0, 0 ≤ j1 ⊦ j ^ j1 % j ^ j0 = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 2 flags: discard

Additional information

Used simplifier rules: pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i);%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%mod-mult-04: j ≠ 0 ⊦ (i * j) % j = 0; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult