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Proof step 32 from proof bib-neg-high (previous step)

i0 < 0 ⊦ b2i(i2b(bits2int(sgn(bitsinvert(uint2bits(1 - 2 * i0)) +1).last ' + false ' + false ' + false ' + false ' + false ' + false ' + false '))) = ~128, i0 * 256 ≠ ~128 ∧ sgn(bitsinvert(uint2bits(abs(2 * i0 - 1))) +1).last

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int2bits inst: name: uint2bits-rec-01 seq: ⊦ 0 < i ∧ i ≠ 1 → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1) subst: [i] → [1 - 2 * i0] flags: rewrite

Additional information

Used simplifier rules: sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%ax-04: ⊦ i + 0 = i; from specification int-basic2%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%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; from specification int-abs%two-zero: ⊦ 2 * i = 0 ↔ i = 0; from specification int-mult%uint2bits-one: ⊦ uint2bits(1) = false + true; from specification int2bits%Two: ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 '; from specification list[bitlista]%invert-zero: ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits); from specification bitopsaux%inv-one-01: ⊦ bitsinvert(true ') = false '; from specification bitopsaux%c: ⊦ boolvar + bits = boolvar ' + bits; from specification list[bitlista]%a: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; from specification list[bitlista]%succ-zero: ⊦ (bits + false ')+1 = bits + true; from specification bitopsaux%Last: ⊦ bits + boolvar = bits + boolvar '; from specification list[bitlista]%sgn-two-01: ⊦ sgn(true ' + true ') = true '; from specification bitopsaux%l: ⊦ boolvar '.last ↔ boolvar; from specification list-last[bitlista] Used terms: 1 - 2 * i0