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Proof step 3 from proof pot-mod-zero (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0
Proof step 5:
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

Rule argument

spec: inst: name: pot-dist-pos seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [j1 - j0, j0, j] flags: rewrite, current

Additional information

Used simplifier rules: Sub-def: ⊦ i + (j - i) = j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2 Used terms: j1 - j0, j0, j