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Proof step 22 from proof fits-law-mul (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
i ≤ i0, j < j0, i0 ≠ 0, 0 ≤ i, 0 ≤ j ⊦ ¬ i0 * j0 ≤ i * j
Proof step 24:
¬(b2i(by1) ≤ 256 ∧ b2i(by2) < 128 ∧ 256 ≠ 0 ∧ 0 ≤ b2i(by1) ∧ 0 ≤ b2i(by2)), 256 * 128 ≤ b2i(by1) * b2i(by2), 0 < b2i(by1) * b2i(by2), 0 ≤ b2i(by1) * b2i(by2) ⊦ b2i(by1) * b2i(by2) = s2i(i2s(b2i(by1) * b2i(by2)))

Rule argument

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

Additional information

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