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Proof step 32 from proof int2bits-add-low (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: ⊦ i ≤ j ∧ j < j0 → i < j0 subst: [i, j, j0] → [ (j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i)) * 2 ^ i + j0, j0, 0] rotate: F spec: int-abs inst: name: fle-01

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + j ≤ i ↔ j ≤ 0;% ⊦ i ≤ 0 → (i * j ≤ 0 ↔ ¬ ¬(i = 0 ∨ 0 ≤ j));% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ 2 ^ i < 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: (j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i)) * 2 ^ i + j0, j0, 0