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Proof step 44 from proof int2bits-add-high (previous step)

j = 1 - 2 ^ i0, 1 = 2 ^ i0 + j, j < 0, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, j * 2 ^ i + j0 < 0, 0 < 2 ^ n→i(# int2bits(~ j)) + j, 0 ≤ (2 ^ n→i(# int2bits(~ j)) + j) * 2 ^ i + j0, 0 ≤ j0 + 2 ^ i, 0 < 2 ^ n→i(# int2bits(1 - j)) + j ⊦ sgn(sgn(uint2bits(2 ^ n→i(# int2bits(~ j)) + j - 1) + fillsgn(i→n(i), int2bits(j0).rest)).rest) = sgn(uint2bits(2 ^ n→i(# int2bits(1 - j)) + j - 1).rest) + fillsgn(i→n(i), int2bits(j0).rest)

User applied rule insert equation

And obtained the following new goals

Proof step 45:
1 = 2 ^ i0 + (1 - 2 ^ i0), 1 - 2 ^ i0 < 0, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, (1 - 2 ^ i0) * 2 ^ i + j0 < 0, 0 < 2 ^ n→i(# int2bits(~(1 - 2 ^ i0))) + (1 - 2 ^ i0), 0 ≤ (2 ^ n→i(# int2bits(~(1 - 2 ^ i0))) + (1 - 2 ^ i0)) * 2 ^ i + j0, 0 ≤ j0 + 2 ^ i, 0 < 2 ^ n→i(# int2bits(1 - (1 - 2 ^ i0))) + (1 - 2 ^ i0) ⊦ sgn(sgn(uint2bits(2 ^ n→i(# int2bits(~(1 - 2 ^ i0))) + (1 - 2 ^ i0) - 1) + fillsgn(i→n(i), int2bits(j0).rest)).rest) = sgn(uint2bits(2 ^ n→i(# int2bits(1 - (1 - 2 ^ i0))) + (1 - 2 ^ i0) - 1).rest) + fillsgn(i→n(i), int2bits(j0).rest)

Rule argument

pos: left 1 flags: discard

Proof step 44 from proof int2bits-add-high (previous step)

User applied rule insert equation

And obtained the following new goals

Rule argument

Additional information