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Proof step 6 from proof gcd-conq-one (previous step)

i * i0 = 1 + ~ j0 * j, 1 = i * i0 + j * j0, gcd(i, j) = 1, 0 ≤ j, 0 ≤ i ⊦ 0 ≤ i0 ∧ j | i * i0 - 1, ∃ i0. 0 ≤ i0 ∧ j | i * i0 - 1

User applied rule insert equation

And obtained the following new goals

Proof step 7:
i * i0 = 1 + ~ j0 * j, 1 = (1 + ~ j0 * j) + j * j0, gcd(i, j) = 1, 0 ≤ j, 0 ≤ i ⊦ 0 ≤ i0 ∧ j | 1 + ~ j0 * j - 1, ∃ i0. 0 ≤ i0 ∧ j | i * i0 - 1

Rule argument

pos: left 1 flags:

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