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Proof step 25 from proof fits-law-mul (previous step)

0 < b2i(by1) * b2i(by2), 0 ≤ b2i(by1) * b2i(by2), 32768 ≤ b2i(by1) * b2i(by2) ⊦ b2i(by1) * b2i(by2) = s2i(i2s(b2i(by1) * b2i(by2))), ¬ b2i(by1) < 0 ∧ ¬ b2i(by2) < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ i < 0 → (0 ≤ i * j ↔ j ≤ 0)
Proof step 27:
b2i(by1) < 0, 0 < b2i(by1) * b2i(by2), b2i(by2) ≤ 0, 32768 ≤ b2i(by1) * b2i(by2) ⊦ b2i(by1) * b2i(by2) = s2i(i2s(b2i(by1) * b2i(by2))), ¬ b2i(by1) < 0 ∧ ¬ b2i(by2) < 0

Rule argument

seq: ⊦ i < 0 → (0 ≤ i * j ↔ j ≤ 0) subst: [j, i] → [b2i(by2), b2i(by1)] rotate: F spec: int-mult inst: name: zero-ge-01

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ i → (0 < i * j ↔ ¬ ¬(0 < j ∧ i ≠ 0));% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i; Used terms: b2i(by2), b2i(by1)