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Proof step 24 from proof gcd-rec-sub-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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(i0), i0 - abs(i)] flags: rewrite, current

Additional information

Used simplifier rules: gcd-neg: ⊦ gcd(~ i, j) = gcd(i, j);%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%subneg: ⊦ i - ~ j = i + j; from specification int-abs%Abs-pos: ⊦ ¬ j < 0 → abs(j) = j; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: abs(i0), i0 - abs(i)