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Proof step 47 from proof bits2int-pos (previous step)

~128 ≤ bits2int(true ' + firstn(# bits0 % 8, bits0)), bits2int(true ' + firstn(# bits0 % 8, bits0)) ≤ 127, 7 < # bits0, # bits0 % 8 ≤ 7, # bits0 % 8 < # bits0, 0 ≤ bits2int(fillsgn(8, sgn(true ' + firstn(# bits0 % 8, bits0))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))) ⊦ (fillsgn(8, sgn(true ' + firstn(# bits0 % 8, bits0))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))).first, bits0 = [], (# bits0 + 1) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first) subst: [bits0, bits] → [bytes2bits(bits2bytes(restn(# bits0 % 8, bits0))), fillsgn(8, sgn(true ' + firstn(# bits0 % 8, bits0)))] rotate: F spec: list inst: bitlista name: first-01

Additional information

Used simplifier rules: ⊦ fillsgn(n, bits) = [] ↔ bits = [] ∧ n = 0;% ⊦ sgn(boolvar ' + bits) ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bytes2bits(bits2bytes(restn(# bits0 % 8, bits0))), fillsgn(8, sgn(true ' + firstn(# bits0 % 8, bits0)))