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Proof step 23 from proof int2bytes-le255 (previous step)

# uint2bits(i) = 9, 127 < i, i ≤ 255, 0 < i, 0 ≤ i, 128 ≤ i, i < 256 ⊦ bits2bytes(firstn(1, uint2bits(i))) + i2b(bits2int(uint2bits(i).rest)) ' = i2b(0) ' + i2b(i - 256) '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ bits ≠ [] → firstn(1, bits) = bits.first '
Proof step 25:
uint2bits(i) ≠ [], # uint2bits(i) = 9, 127 < i, i ≤ 255, 0 < i, 0 ≤ i, 128 ≤ i, i < 256 ⊦ bits2bytes(uint2bits(i).first ') + i2b(bits2int(uint2bits(i).rest)) ' = i2b(0) ' + i2b(i - 256) '

Rule argument

seq: ⊦ bits ≠ [] → firstn(1, bits) = bits.first ' subst: [bits] → [uint2bits(i)] rotate: F spec: list-del inst: bitlista name: firstN-one

Additional information

Used simplifier rules: 0 ≤ i ⊦ uint2bits(i) ≠ []; Used terms: uint2bits(i)