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Proof step 7 from proof div-twopot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-zero seq: 0 < j, 0 ≤ i, i < j ⊦ i / j = 0 subst: [j, i] → [2 ^ j, 2 ^ (i0 + j)] flags: rewrite

Additional information

Used simplifier rules: pot2-pos: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;%ls-pos-2pot: ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0);%two-lsz: ⊦ ¬ 2 ^ i < 0;%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ 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%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs Used terms: 2 ^ j, 2 ^ (i0 + j)