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Proof step 20 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(lastn(8, uint2bits(i)))) ' = i2b(0) ' + i2b(i - 256) '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ # bits = n + 1 → lastn(n, bits) = bits.rest
Proof step 22:
# uint2bits(i) = 8 + 1, # 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) '

Rule argument

seq: ⊦ # bits = n + 1 → lastn(n, bits) = bits.rest subst: [bits, n] → [uint2bits(i), 8] rotate: F spec: list-del inst: bitlista name: lastN-rest-01

Additional information

Used terms: uint2bits(i), 8