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Proof step 26 from proof congmod-inverse-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
(i * i1) |%| j = 1, gcd(i, j) = 1, i0 < 0, ≡mod(i * i0, 1, j), 0 ≤ j, 0 ≤ i, 0 < i1, 0 < j, 0 ≤ i1 ⊦ ≡mod(i * i1, 1, j), ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs