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Proof step 8 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 ⊦ j = 0, ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0 ∧ i0 < j

User applied rule cut formula

And obtained the following new goals

Proof step 9:
gcd(i, j) = 1, ≡mod(i * i0, 1, j), 0 ≤ i0, 0 ≤ i, 0 < j, j ≤ i0, 0 < i0 ⊦ i = 0, j = 0, ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0 ∧ i0 < j

Rule argument

fma: i = 0

Additional information

Used simplifier rules: cong-one: ⊦ ≡mod(i, j, 1);%gcd-zero-03: ⊦ i ≠ 0 → gcd(i, 0) = abs(i); from specification int-gcd%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%gcd-com: ⊦ gcd(i, j) = gcd(j, i); from specification int-gcd%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%bet-01: ⊦ 0 ≤ i → (i < 1 ↔ i = 0); from specification int-abs Used formulas: i = 0