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Proof step 4 from proof congmod-inverse-smallest (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 5:
gcd(i, j) = 1, ≡mod(i * i0, 1, j), 0 ≤ i0, 0 ≤ i, 0 < j ⊦ ≡mod(i * i0, 1, j) ∧ 0 ≤ i0 ∧ i0 < j, ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0 ∧ i0 < j

Rule argument

pos: right 1 terms: i0 abort: F discard: F computed: T

Additional information

Used terms: i0