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Proof step 8 from proof pot2-ls-pred-01 (previous step)

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

Additional information

Used simplifier rules: two-leone: ⊦ 2 ^ i ≤ 1 ↔ i < 1;%two-lsz: ⊦ ¬ 2 ^ i < 0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s) Used terms: 2 ^ ~ i