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Proof step 37 from proof div-div-pred-01 (previous step)

(8 * i1) % 8 = 0, 8 * i1 + j0 + j1 * 2 < 0, 8 * i1 + j0 + j1 * 2 < ~7, abs(j0) < 2, abs(j1) < 4, i1 * 4 + j1 < 0, 8 * i1 < 0, j0 + j1 * 2 < 0, 0 < 8, j0 ≤ 0, j1 ≤ 0, i1 ≤ 0, i1 * 4 + j1 ≤ ~3 ⊦ i1 = (8 * i1) / 8 + (j0 + j1 * 2) / 8

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
i1 * 4 + j1 < 0, abs(j1) < 4, abs(j0) < 2, 8 * i1 + j0 + j1 * 2 < ~7, 8 * i1 + j0 + j1 * 2 < 0, j0 + j1 * 2 < 0, i1 < 0, i1 * 4 + j1 ≤ ~3, j1 ≤ 0, j0 ≤ 0 ⊦ (j0 + j1 * 2) / 8 = 0

Rule argument

Additional information

Used simplifier rules: mod-zero-num: i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0;%div-mult-num: j ≠ 0, j0 % j = 0 ⊦ (i * (* j0)) / (* j) = i * j0 / j;%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ 0 < i → (i * j < 0 ↔ j < 0); (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i = i + j ↔ j = 0; (s)% ⊦ 1 * i = i; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult