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Proof step 25 from proof congmod-inverse-pos (previous step)

(i * i1) |%| j = 1, gcd(i, j) = 1, i0 < 0, ≡mod(i * i0, 1, j), 0 ≤ j, 0 ≤ i, 0 < i1, i0 < i1, 0 < j ⊦ ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0

User applied rule exists right

And obtained the following new goals

Proof step 26:
(i * i1) |%| j = 1, gcd(i, j) = 1, i0 < 0, ≡mod(i * i0, 1, j), 0 ≤ j, 0 ≤ i, 0 < i1, i0 < i1, 0 < j ⊦ ≡mod(i * i1, 1, j) ∧ 0 ≤ i1, ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0

Rule argument

pos: right 1 terms: i1 abort: F discard: F computed: F

Additional information

Used terms: i1