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Proof step 11 from proof ls-mult-2pot (previous step)

i1 < j, i1 < 0, j * 2 ^ i < 2 ^ (i1 + i), 0 ≤ i1 + i, 0 ≤ i, 0 < j, i1 + 1 < j, j * 2 ^ i < 2 ^ i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ 0 < i → (j * i < i ↔ j < 1)

Rule argument

spec: int-mult inst: name: ls-same-04 seq: ⊦ 0 < i → (j * i < i ↔ j < 1) subst: [i, j] → [2 ^ i, j] flags: rewrite

Additional information

Used simplifier rules: pot2-pos: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;%pot2-pos: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%num-between: i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; from specification int-basic2 Used terms: 2 ^ i, j