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Proof step 15 from proof ls-mult-2pot (previous step)

0 < j, 0 ≤ i, 0 ≤ i1, 0 ≤ i1 + i ⊦ j * 2 ^ i < 2 ^ i1 * 2 ^ i ↔ j < 2 ^ i1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 0 < j → (i * j < i0 * j ↔ i < i0)

Rule argument

spec: int-mult name: ls-pos-01 seq: ⊦ 0 < j → (i * j < i0 * j ↔ i < i0) subst: [i0, j, i] → [2 ^ i1, 2 ^ i, j] flags: <all paths>

Additional information

Used simplifier rules: grz: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j); Used terms: 2 ^ i1, 2 ^ i, j