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Proof step 13 from proof cast-mod-neg-low (previous step)

i→n(i) ≤ # int2bits(j), 0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0 ⊦ j = ~1, bits2int(lastn(i→n(i), int2bits(j))) = j % 2 ^ i + 2 ^ i

User applied rule cut formula

And obtained the following new goals

Proof step 14:
i = 1, i→n(i) ≤ # int2bits(j), 0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0 ⊦ j = ~1, bits2int(lastn(i→n(i), int2bits(j))) = j % 2 ^ i + 2 ^ i
Proof step 19:
i→n(i) ≤ # int2bits(j), 0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0 ⊦ i = 1, j = ~1, bits2int(lastn(i→n(i), int2bits(j))) = j % 2 ^ i + 2 ^ i

Rule argument

fma: i = 1

Additional information

Used formulas: i = 1