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Proof step 1 from proof gcdhex (conclusion)

0 ≤ i, 0 ≤ j, j ≤ i ⊦ ∃ i0, j0. gcd(i, j) = i * i0 + j * j0

User applied rule induction

And obtained the following new goals

Proof step 2:
0 ≤ i ∧ 0 ≤ j ∧ j ≤ i, ∀ i0, j. i→n(i0) < i→n(i) → 0 ≤ i0 ∧ 0 ≤ j ∧ j ≤ i0 → (∃ i1, j0. gcd(i0, j) = i0 * i1 + j * j0) ⊦ ∃ i0, j0. gcd(i, j) = i * i0 + j * j0

Rule argument

indvar: i→n(i) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(i)