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Proof step 6 from proof fits-law-mul (previous step)

b2i(by1) * b2i(by2) < ~32768, b2i(by1) * 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 7:
⊦ i * j < 0 ↔ 0 < i ∧ j < 0 ∨ i < 0 ∧ 0 < j
Proof step 8:
b2i(by1) * b2i(by2) < ~32768, 0 < b2i(by1) ∧ b2i(by2) < 0 ∨ b2i(by1) < 0 ∧ 0 < b2i(by2) ⊦ b2i(by1) * b2i(by2) = s2i(i2s(b2i(by1) * b2i(by2)))

Rule argument

seq: ⊦ i * j < 0 ↔ 0 < i ∧ j < 0 ∨ i < 0 ∧ 0 < j subst: [j, i] → [b2i(by2), b2i(by1)] rotate: F spec: int-mult inst: name: zero-ls-case

Additional information

Used simplifier rules: ⊦ i * j = j * i; Used terms: b2i(by2), b2i(by1)