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Proof step 12 from proof ls-mult-2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ 0 < i → (j * i < i ↔ j < 1)

Rule argument

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

Additional information

Used simplifier rules: grz: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1 Used terms: 2 ^ i, j