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Proof step 8 from proof pot2-le-pred (previous step)

2 ^ i < 1 / 2 ^ abs(i - 1), i ≤ 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 1 < j → 1 / j = 0

Rule argument

spec: int-div inst: name: one-04 seq: ⊦ 1 < j → 1 / j = 0 subst: [j] → [2 ^ abs(i - 1)] flags: rewrite

Additional information

Used simplifier rules: pot2-pos-01: ⊦ 1 < 2 ^ i ↔ 0 < i;%2pot-leone: ⊦ 2 ^ i < 1 ↔ i < 0;%pot2-pos-01: ⊦ 1 < 2 ^ i ↔ 0 < i;%two-lsz: ⊦ ¬ 2 ^ i < 0;%abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs%sub-eq: ⊦ i - j = i0 ↔ i = i0 + 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%sub-eq-01: ⊦ i = j → i - j = 0; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs Used terms: 2 ^ abs(i - 1)