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Proof step 9 from proof pot-zero-01 (previous step)

0 < i, j < 0 ⊦ 1 / i ^ ~ j = 0 ↔ 1 < i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div name: div-zero seq: 0 < j, 0 ≤ i, i < j ⊦ i / j = 0 subst: [j, i] → [i ^ ~ j, 1] flags: <all paths>

Additional information

Used simplifier rules: grz: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);%eqone-02: ⊦ i ^ ~ j = 1 ∧ j < 0 → abs(i) = 1;%one-01: ⊦ 1 ^ j = 1;%one-01: ⊦ 1 ^ j = 1;%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ 0 < i → (i ≤ 1 ↔ i = 1); (s)%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1% ⊦ i ≤ ~ j ↔ i + j ≤ 0; (s)% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ 0 < i ∧ 0 < j → (i / j = 0 ↔ i < j); (s)% ⊦ 1 < i → abs(i) = i; (s) Used terms: i ^ ~ j, 1