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Proof step 86 from proof int2bits-add-low (previous step)

0 < i, j < 0, j0 < 0, 0 < 2 ^ (i - 1) + j0, 0 ≤ i, 0 ≤ 2 * 2 ^ (i - 1) * j + 2 ^ n→i(# int2bits(~(2 * 2 ^ (i - 1) * j + j0))) + j0, 2 * 2 ^ (i - 1) * j + j0 < 0, 0 < 2 ^ (i - 1) * (2 * j + 1) + j0 ⊦ sgn(uint2bits(2 * 2 ^ (i - 1) * j + 2 ^ n→i(# int2bits(~(2 * 2 ^ (i - 1) * j + j0))) + j0).rest) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i ∧ j < 0 ∧ j0 ≤ 0 → ¬ 0 < i * j + j0 subst: [j0, j, i] → [j0, 2 * j + 1, 2 ^ (i - 1)] rotate: F spec: int-mult inst: name: zero-gr-add-01

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ 2 ^ i < 0;% ⊦ i < 0 ∧ j0 < j ∧ 0 ≤ j → i * j + j0 < 0;% ⊦ i < j → ¬ j < i; Used terms: j0, 2 * j + 1, 2 ^ (i - 1)