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Proof step 6 from proof congmod-inverse-smallest (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 7:
gcd(i, j) = 1, ≡mod(i * i0, 1, j), 0 ≤ i0, 0 ≤ i, 0 < j, j ≤ i0, 0 < i0 ⊦ j = 0, ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0 ∧ i0 < j

Rule argument

fma: j = 0

Additional information

Used simplifier rules: cong-zero: ⊦ ≡mod(i, j, 0) ↔ i = j;%gcd-zero-04: ⊦ gcd(i, 0) = abs(i); from specification int-gcd%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used formulas: j = 0