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Proof step 10 from proof denom-not-zero (previous step)

gcd(i, i0) ≠ 0, abs(i0) ≠ 0, 0 ≤ gcd(i, i0), abs(i0) / gcd(i, i0) = 0 ⊦ i = 0, i0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
abs(i) < abs(j) ⊦ i / j = 0
Proof step 12:
abs(abs(i0)) < abs(gcd(i, i0)), gcd(i, i0) ≠ 0, abs(i0) ≠ 0, 0 ≤ gcd(i, i0), 0 = 0 ⊦ i = 0, i0 = 0

Rule argument

seq: abs(i) < abs(j) ⊦ i / j = 0 subst: [j, i] → [gcd(i, i0), abs(i0)] rotate: F spec: int-div inst: name: div-zero-02

Additional information

Used simplifier rules: ⊦ 0 ≠ j → (i / j = 0 ↔ abs(i) < abs(j));% ⊦ abs(abs(i)) = abs(i);% ⊦ abs(gcd(i, j)) = gcd(i, j);% ⊦ abs(i) = 0 ↔ i = 0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: gcd(i, i0), abs(i0)