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Proof step 9 from proof div2 (previous step)

i0 < ~1, i0 < 0 ⊦ 1 / 2 ^ ~(i0 + 1) = 0, 1 / 2 ^ ~(i0 + 1) = ~1, 2 ^ ~(i0 + 1) = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 1 < j → 1 / j = 0

Rule argument

spec: int-div name: one-04 seq: ⊦ 1 < j → 1 / j = 0 subst: [j] → [2 ^ ~(i0 + 1)] flags: <all paths>

Additional information

Used simplifier rules: 2pot-leone: ⊦ 2 ^ i < 1 ↔ i < 0;% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)% ⊦ ~ i < 0 ↔ 0 < i; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ i < j → (j ≤ i ↔ false); (as)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: 2 ^ ~(i0 + 1)