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Proof step 29 from proof bib-neg-high (previous step)

i0 < 0 ⊦ b2i(i2b(bits2int(((((((int2bits(2 * i0 - 1).last ' + false ') + false ') + false ') + false ') + false ') + false ') + false '))) = ~128, i0 * 256 ≠ ~128 ∧ int2bits(2 * i0 - 1).last

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int2bits inst: name: int2bits-neg seq: ⊦ i < 0 → int2bits(i) = sgn(bitsinvert(uint2bits(abs(i))) +1) subst: [i] → [2 * i0 - 1] flags: rewrite

Additional information

Used simplifier rules: sub-ls: ⊦ i - j < i0 ↔ i < j + 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%nummult-ls: ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i); from specification int-div%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 2 * i0 - 1