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Proof step 49 from proof bib-neg-high (previous step)

i0 < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i0 * 256 - 128))))) = ~128, i0 * 256 = (2 * i0 - 1) * 128 + 128, i0 * 256 ≠ ~128 ∧ lastn(8, int2bits(i0 * 256 - 128)).first

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-sub-split seq: ⊦ (i - j) * j0 = i * j0 - j * j0 subst: [j0, j, i] → [128, 1, 2 * i0] flags: rewrite

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%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%eq-neg: ⊦ i < 0 → (i * j = i * j0 ↔ j = j0); from specification int-mult Used terms: 128, 1, 2 * i0