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Proof step 25 from proof sis-neg-high (previous step)

i0 < 0 ⊦ i0 = 0, s2i(i2s(bits2int(lastn(16, int2bits(65536 * i0 - 32768))))) = ~32768

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 65536 * i0 - 32768 = (2 * i0 - 1) * 2 ^ 15

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i * j + i = i * (j + 1);% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i < 0 → (i * j = i * j0 ↔ j = j0); Used formulas: 65536 * i0 - 32768 = (2 * i0 - 1) * 2 ^ 15