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Proof step 118 from proof bits2bits-sgn (previous step)

¬ false ∈ firstn(# bits - 8, bits) ∧ firstn(# bits - 8, bits) ≠ [], firstn(# bits - 8, bits) + lastn(8, bits) = bits, bits2int(lastn(8, bits)) ≤ 127, 8 < # bits, 0 ≤ bits2int(lastn(8, bits)), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ bits = [], true ' + byte2bits(i2b(bits2int(lastn(8, bits)))) = sgn(true ' + lastn(8, bits)), false ∈ firstn(# bits - 8, bits), false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] ∧ (bits.first ↔ ¬ boolvar) → sgn(boolvar ' + bits) = boolvar ' + bits subst: [bits, boolvar] → [lastn(8, bits), true] rotate: F spec: bitopsaux inst: name: sgn-base-03

Additional information

Used simplifier rules: ⊦ firstn(n, bits) = [] ↔ n = 0;% ⊦ n < m → m - n ≠ 0;% ⊦ lastn(n, bits) = [] ↔ n = 0;%bits ≠ [] ⊦ 0 ≤ bits2int(bits) → ¬ bits.first; Used terms: lastn(8, bits), true