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Proof step 9 from proof bits2bits-sgn (previous step)

# bits ≤ 8, ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ bits = [], sgn(fillsgn(8, int2bits(b2i(i2b(bits2int(bits)))))) = sgn(bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i
Proof step 11:
~128 ≤ bits2int(bits) ∧ bits2int(bits) ≤ 127, # bits ≤ 8, ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ bits = [], sgn(fillsgn(8, int2bits(bits2int(bits)))) = sgn(bits)

Rule argument

seq: ~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i subst: [i] → [bits2int(bits)] rotate: F spec: byte inst: name: num-ibbi

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ # bits ≤ 8 ∧ bits ≠ [] → ¬ bits2int(bits) < ~128;% ⊦ # bits ≤ 8 ∧ bits ≠ [] → ¬ 127 < bits2int(bits); Used terms: bits2int(bits)