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Proof step 91 from proof uint2bits-restsgn (previous step)

2 * i0 < (2 * 2) * 2 ^ i, 0 ≤ 2 ^ i, 2 ^ i < 2 * i0, i0 < 2 ^ i, 1 < 2 ^ i, 0 < 2 ^ i, 0 ≤ i0, 0 < i0, 1 < i, 1 < i0, 0 < i, 0 ≤ i, ∀ j0, i. i→n(j0) < i→n(2 * i0 + 0) → 0 < i ∧ 0 ≤ j0 ∧ 2 ^ i < j0 ∧ j0 < 2 * 2 ^ i → sgn(uint2bits(2 ^ (i + 2) - j0).rest) = uint2bits(2 ^ (i + 2) - j0).rest ⊦ ((2 * 2) * 2 ^ i - 2 * i0) / 2 = 2 * 2 ^ i - i0, (2 * 2) * 2 ^ i = 1 + 2 * i0, sgn(uint2bits(((2 * 2) * 2 ^ i - 2 * i0) / 2).rest + (((2 * 2) * 2 ^ i - 2 * i0) % 2 = 1)') = uint2bits(((2 * 2) * 2 ^ i - 2 * i0) / 2).rest + (((2 * 2) * 2 ^ i - 2 * i0) % 2 = 1)'

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i * j - i * j0 = i * (j - j0) subst: [j0, j, i] → [i0, 2 * 2 ^ i, 2] rotate: F spec: int-mult inst: name: dist-sub-merge

Additional information

Used simplifier rules: j ≠ 0 ⊦ (i * j) / j = i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i0, 2 * 2 ^ i, 2