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Proof step 55 from proof bits2int-pos (previous step)

7 < # bits0, # bits0 % 8 ≤ 7, # bits0 % 8 < # bits0, bits2int(fillsgn(8, int2bits(b2i(i2b(bits2uint(firstn(# bits0 % 8, bits0)))))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))) < 0 ⊦ bits0 = [], (# bits0 + 1) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i
Proof step 57:
¬(~128 ≤ bits2uint(firstn(# bits0 % 8, bits0)) ∧ bits2uint(firstn(# bits0 % 8, bits0)) ≤ 127), 7 < # bits0, # bits0 % 8 ≤ 7, # bits0 % 8 < # bits0, bits2int(fillsgn(8, int2bits(b2i(i2b(bits2uint(firstn(# bits0 % 8, bits0)))))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))) < 0 ⊦ bits0 = [], (# bits0 + 1) % 8 = 0
Proof step 60:
~128 ≤ bits2uint(firstn(# bits0 % 8, bits0)) ∧ bits2uint(firstn(# bits0 % 8, bits0)) ≤ 127, 7 < # bits0, # bits0 % 8 ≤ 7, # bits0 % 8 < # bits0, bits2int(fillsgn(8, int2bits(bits2uint(firstn(# bits0 % 8, bits0)))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))) < 0 ⊦ bits0 = [], (# bits0 + 1) % 8 = 0

Rule argument

seq: ~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i subst: [i] → [bits2uint(firstn(# bits0 % 8, bits0))] rotate: F spec: byte inst: name: num-ibbi

Additional information

Used terms: bits2uint(firstn(# bits0 % 8, bits0))