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Proof step 7 from proof gcd-rec-sub (previous step)

0 < i, 0 < i0, 1 < i0 + i ⊦ gcd(i0 + i, i) = gcd(i, i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < j ∧ 0 ≤ i → gcd(i, j) = gcd(j, i % j)
Proof step 9:
1 < i0 + i, 0 < i0, 0 < i, 0 ≤ i0 + i ⊦ gcd(i, (i0 + i) % i) = gcd(i, i0)

Rule argument

spec: <toplevel> name: gcd-rec-pos seq: ⊦ 0 < j ∧ 0 ≤ i → gcd(i, j) = gcd(j, i % j) subst: [j, i] → [i, i0 + i] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i; (s) Used terms: i, i0 + i