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Proof step 23 from proof congmod-inverse-smallest (previous step)

abs(1) < j, i * i0 = i1 + 1, gcd(i, j) = 1, 0 ≤ i0, 0 < i, i0 |%| j < j, i0 |%| j < i0, 0 ≤ i0 |%| j, 0 < j, j ≤ i0, 0 < i0, j | i1 ⊦ i = 0, j = 0, (i * i0 |%| j) |%| j = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
i * i0 = i1 + 1, gcd(i, j) = 1, 0 < i0, 1 < i0, 0 ≤ i0, 0 < i, i0 |%| j < j, i0 |%| j < i0, 0 ≤ i0 |%| j, j ≤ i0, j | i1, 0 < j, 1 < j ⊦ i = 0, j = 0, (i * i0 |%| j) |%| j = 1

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]