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Proof step 20 from proof bib-neg-high (previous step)

i0 * 256 + j0 < 0, i0 ≤ 0, j0 ≤ 0, ~128 ≤ j0, i0 * 256 + j0 ≤ ~256, abs(j0) < 256 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i0 * 256 + j0))))) = j0, ~256 ≠ i0 * 256 + j0 ∧ lastn(8, int2bits(i0 * 256 + j0)).first, i0 < 0 ∧ j0 < 0 ∧ ~128 ≠ j0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i0 < 0

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%ax-04: ⊦ i + 0 = 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%numlsledel-01: i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1%forward-lels: ⊦ 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%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs Used formulas: i0 < 0