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Proof step 34 from proof congmod-inverse (previous step)

gcd(i, j) = 1, ~1 = (i * i0) % abs(j), 0 < i0, i < 0, i < i0 ⊦ j = 0, j | i * i0 - 1, ∃ i0. ≡mod(i * i0, 1, j)

User applied rule exists right

And obtained the following new goals

Proof step 35:
gcd(i, j) = 1, ~1 = (i * i0) % abs(j), 0 < i0, i < 0, i < i0 ⊦ j = 0, j | i * i0 - 1, ≡mod(i * ~ i0, 1, j), ∃ i0. ≡mod(i * i0, 1, j)

Rule argument

pos: right 3 terms: ~ i0 abort: F discard: F computed: F

Additional information

Used terms: ~ i0