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Proof step 10 from proof congmod-inverse-smallest (previous step)

gcd(i, j) = 1, 0 < j, j ≤ i0, 0 < i0, ≡mod(i * i0, 1, j), 0 ≤ i0, 0 < i ⊦ i = 0, j = 0, ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0 ∧ i0 < j

User applied rule exists right

And obtained the following new goals

Proof step 11:
gcd(i, j) = 1, 0 < j, j ≤ i0, 0 < i0, ≡mod(i * i0, 1, j), 0 ≤ i0, 0 < i ⊦ i = 0, j = 0, ≡mod(i * i0 |%| j, 1, j) ∧ 0 ≤ i0 |%| j ∧ i0 |%| j < j

Rule argument

pos: right 3 terms: i0 |%| j abort: F discard: T computed: F

Additional information

Used terms: i0 |%| j