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Proof step 24 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 ⊦ 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 rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ j0 < 0 ∧ 0 < i ∧ abs(j0) ≤ 2 ^ (i - 1) ∧ 0 < j → uint2bits(j * 2 ^ i + j0) = uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))
Proof step 26:
¬(j0 < 0 ∧ 0 < i ∧ abs(j0) ≤ 2 ^ (i - 1) ∧ 0 < j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i)), 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 ⊦ 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
Proof step 43:
j0 < 0 ∧ 0 < i ∧ abs(j0) ≤ 2 ^ (i - 1) ∧ 0 < j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i), 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 ⊦ sgn((uint2bits(j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i) - 1) + fillsgn(i→n(i), int2bits(j0))).rest) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0)), j * 2 ^ i + j0 = 0

Rule argument

name: uint2bits-add-low-01 rotate: F subst: [j0, i, j] → [j0, i, j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i)]

Additional information

Used terms: j0, i, j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i)