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Proof step 14 from proof congmod-inverse-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
i0 < 0, 0 < j, 1 < j, 0 ≤ j, ≡mod(i0, 1, j) ⊦ ∃ i. ≡mod(i, 1, j) ∧ 0 ≤ i

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%gcd-com: ⊦ gcd(i, j) = gcd(j, i); from specification int-gcd%gcd-one-01: ⊦ gcd(i, 1) = 1; from specification int-gcd