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Proof step 34 from proof gcd-mult-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
j ≤ i, 0 ≤ i, 0 < i1, 0 < i, 0 < j, 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 < i0 ∧ 0 < i2 ∧ 0 ≤ j0 → gcd(i2 * i0, j0 * i0) = gcd(i2, j0) * i0 ⊦ j = 0, gcd(j * i1, i % j * i1) = gcd(j, i % j) * i1

Rule argument

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%labs: ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j); from specification intnat