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Proof step 41 from proof congmod-inverse (previous step)

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

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 2 flags: rotate, discard

Additional information

Used simplifier rules: div-abs: ⊦ i | abs(i) * j; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult