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Proof step 30 from proof div-div-pred-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i1 = 0

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%num-between: i + 1 = i0 ⊦ (* i) < j → (j ≤ (* i0) ↔ j = i0); from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%minus-add: i < 0 ⊦ (* i) + j = j - ~ i; from specification int-abs%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%numlsledel: j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); from specification int-abs%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1%minus-one: ⊦ i < 0 → (~2 < i ↔ i = ~1); from specification int-basic1%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1 Used formulas: i1 = 0