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Proof step 76 from proof gcd-rec-sub-01 (previous step)

abs(i0) < abs(i), 0 < i, i0 < 0 ⊦ i0 = 0, gcd(abs(i), abs(i) - abs(i0)) = gcd(abs(i0), abs(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 77:
⊦ 0 < i ∧ i < j → gcd(i, j) = gcd(j, j - i)

Rule argument

spec: int-gcd inst: name: gcd-rec-sub-02 seq: ⊦ 0 < i ∧ i < j → gcd(i, j) = gcd(j, j - i) subst: [j, i] → [abs(i), abs(i0)] flags: rewrite, current

Additional information

Used simplifier rules: gcd-neg: ⊦ gcd(~ i, j) = gcd(i, j);%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%subneg: ⊦ i - ~ j = i + j; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs Used terms: abs(i), abs(i0)