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Proof step 48 from proof bits2bits-sgn (previous step)

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 = [], sgn(false ' + byte2bits(i2b(bits2int(lastn(8, bits))))) = sgn(false ' + lastn(8, bits)), true ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))), true ∈ 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) = sgn(bits) subst: [bits, boolvar] → [byte2bits(i2b(bits2int(lastn(8, bits)))), false] rotate: F spec: bitopsaux inst: name: sgn-rec-01

Additional information

Used simplifier rules: byte2bits-empty: ⊦ byte2bits(by) ≠ [];%byte2bits-first: ⊦ byte2bits(by).first ↔ b2i(by) < 0;% ⊦ 0 ≤ i ∧ i ≤ 127 → b2i(i2b(i)) = i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: byte2bits(i2b(bits2int(lastn(8, bits)))), false