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Proof step 45 from proof bib-neg-high (previous step)

i0 * 2 * 128 + 128 = 0, i0 * 256 = ~128, i0 < 0 ⊦ i0 = 0, b2i(i2b(bits2int(true ' + false ' + false ' + false ' + false ' + false ' + false ' + false '))) = ~128

User applied rule cut formula

And obtained the following new goals

Proof step 46:
i0 * 2 * 128 + 128 = 0, i0 * 256 = ~128, i0 < 0 ⊦ i0 * 2 * 128 + 128 = 128 * (i0 * 2 + 1), i0 = 0, b2i(i2b(bits2int(true ' + false ' + false ' + false ' + false ' + false ' + false ' + false '))) = ~128

Rule argument

fma: i0 * 2 * 128 + 128 = 128 * (i0 * 2 + 1)

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 0); from specification int-mult%eq-one-neg: ⊦ i * j = ~1 ↔ abs(i) = 1 ∧ i = ~ j; from specification int-mult%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs Used formulas: i0 * 2 * 128 + 128 = 128 * (i0 * 2 + 1)