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Proof step 35 from proof gcd-mult-pos (previous step)

0 < j, 0 < i, 0 < i1, 0 ≤ i, j ≤ i, ∀ j0, i0, i2. i→n(j0 * i0 + i2 * i0) < i→n(j * i1 + i * i1) → 0 < i2 ∧ 0 < i0 ∧ 0 ≤ j0 → gcd(i2 * i0, j0 * i0) = gcd(i2, j0) * i0 ⊦ gcd(j * i1, i % j * i1) = gcd(j, i % j) * i1, i1 = 0, j = 0, i→n(i % j * i1 + j * i1) < i→n(j * i1 + i * i1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
0 < i1, 0 < i, 0 < j, j ≤ i, 0 ≤ i, abs(j * i1 + i * i1) ≤ abs(i % j * i1 + j * i1), ∀ j0, i0, i2. i→n(j0 * i0 + i2 * i0) < i→n(j * i1 + i * i1) → 0 < i2 ∧ 0 < i0 ∧ 0 ≤ j0 → gcd(i2 * i0, j0 * i0) = gcd(i2, j0) * i0 ⊦ gcd(j * i1, i % j * i1) = gcd(j, i % j) * i1, i1 = 0, j = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j); (s)