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Proof step 5 from proof congmod-inverse-smallest (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
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

Rule argument

Additional information

Used simplifier rules: forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs