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Proof step 35 from proof gcd-rec-sub-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: gcd-same-01 seq: ⊦ 0 < j → gcd(j, j) = j subst: [j] → [abs(i0)] flags: rewrite, current

Additional information

Used simplifier rules: gcd-zero-03: ⊦ i ≠ 0 → gcd(i, 0) = abs(i);%gcd-same-01: ⊦ 0 < j → gcd(j, j) = j;%gcd-zero-03: ⊦ i ≠ 0 → gcd(i, 0) = abs(i);%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%sub-sub-03: ⊦ i - i = 0; from specification int-abs Used terms: abs(i0)