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Proof step 16 from proof mod-two-ge-01 (previous step)

2 ^ (i0 + j) = i1 + 1, 0 ≤ j, 0 < i0, 0 < i0 + j ⊦ i1 + 1 = 2 ^ j * (i1 / 2 ^ j + 1), i1 + 1 = 2 ^ j * 2 ^ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: pot-dist-pos seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [j, i0, 2] flags: rewrite, current

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j, i0, 2