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Proof step 75 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 ≤ 2 ^ n→i(# int2bits(~(j * 2 ^ i + j0))) + j * 2 ^ i + j0 ⊦ sgn(uint2bits(2 ^ n→i(# int2bits(~(j * 2 ^ i + j0))) + j * 2 ^ i + j0).rest) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0)), j * 2 ^ i + j0 = 0, 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i) * 2 ^ i = 2 ^ n→i(# int2bits(~(j * 2 ^ i + j0)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [i, n→i(# int2bits(~(j * 2 ^ i + j0))) - i, 2] rotate: T spec: int-pot inst: name: pot-dist-pos

Additional information

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