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Proof step 47 from proof ex-modeq-half (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%mod-less-01: ⊦ 0 < j → i % j < j; from specification int-div%ax-04: ⊦ i + 0 = i; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%minus-sub: ⊦ ~(i - j) = j - i; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs