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Proof step 60 from proof int2bits-add-low (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 61:
⊦ i + (j - i0) = i + j - i0
Proof step 62:
0 ≤ 2 ^ n→i(# int2bits(~(j - 1) - 1)) + (j - 1), 0 ≤ j0 + 2 ^ (i - 1), 0 < 2 ^ (i - 1) + j0, j0 < 0, j < 0, 0 < i, j * 2 ^ i + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, 0 < 2 ^ n→i(# int2bits(~(j - 1) - 1)) + j, 0 ≤ 2 ^ i * (2 ^ n→i(# int2bits(~(j - 1) - 1)) + j) + j0 ⊦ j * 2 ^ i + j0 = 0, sgn(int2bits(2 ^ n→i(# int2bits(~(j - 1) - 1)) + (j - 1)).rest + fillsgn(i→n(i), int2bits(j0))) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))

Rule argument

seq: ⊦ i + (j - i0) = i + j - i0 subst: [i0, j, i] → [1, j, 2 ^ n→i(# int2bits(~(j - 1) - 1))] rotate: T spec: int-abs inst: name: sub-add-01

Additional information

Used terms: 1, j, 2 ^ n→i(# int2bits(~(j - 1) - 1))