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Proof step 22 from proof gcd-conq-one (previous step)

1 = i0 * i + j * j0, gcd(i, j) = 1, i0 < 0, 0 < i, j * j0 + i0 < 0, i0 * i + j * j0 ≤ j * j0 + i0, 0 ≤ j ⊦ i = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: rotate, discard

Additional information

Used simplifier rules: ⊦ 1 ≤ i ↔ 0 < i; (s)% ⊦ i < j → ¬ j < i; (s)