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Proof step 39 from proof ex-modeq-half (previous step)

i0 % j = j0 * j + j, j0 < j, j0 < 0, odd(j), 0 < j, j / 2 < i0 % j, 0 ≤ i0 % j ⊦ j = 0, ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2, (i0 % j - j) |%| j = i0 % j ∧ j ≤ i0 % j + j / 2

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: j0 * j + j < 0

Additional information

Used simplifier rules: lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs Used formulas: j0 * j + j < 0