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Proof step 30 from proof fits-law-mul (previous step)

~256 * ~128 ≤ b2i(by1) * b2i(by2), b2i(by1) < 0, b2i(by2) < 0 ⊦ b2i(by1) * b2i(by2) = s2i(i2s(b2i(by1) * b2i(by2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
i < 0, j < 0, i0 ≤ i, j0 < j ⊦ ¬ i0 * j0 ≤ i * j
Proof step 32:
¬(b2i(by1) < 0 ∧ b2i(by2) < 0 ∧ ~256 ≤ b2i(by1) ∧ ~128 < b2i(by2)), ~256 * ~128 ≤ b2i(by1) * b2i(by2), b2i(by1) < 0, b2i(by2) < 0 ⊦ b2i(by1) * b2i(by2) = s2i(i2s(b2i(by1) * b2i(by2)))

Rule argument

seq: i < 0, j < 0, i0 ≤ i, j0 < j ⊦ ¬ i0 * j0 ≤ i * j subst: [j, i, j0, i0] → [b2i(by2), b2i(by1), ~128, ~256] rotate: F spec: int-mult inst: name: pnle-neg

Additional information

Used terms: b2i(by2), b2i(by1), ~128, ~256