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Proof step 11 from proof int2bytes-rec-pos (previous step)

uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, 255 < i, 0 < i, 0 ≤ i ⊦ bits2bytes(uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest) = bits2bytes(uint2bits(i / 256)) + bits2bytes(int2bits(i % 256)).last '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ 8 < # bits → bits2bytes(bits) = bits2bytes(firstn(# bits - 8, bits)) + i2b(bits2int(lastn(8, bits)))
Proof step 13:
¬ 8 < #(uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest), uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, 255 < i, 0 < i, 0 ≤ i ⊦ bits2bytes(uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest) = bits2bytes(uint2bits(i / 256)) + bits2bytes(int2bits(i % 256)).last '
Proof step 21:
8 < #(uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest), uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, 255 < i, 0 < i, 0 ≤ i ⊦ bits2bytes(firstn(#(uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest) - 8, uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest)) + i2b(bits2int(lastn(8, uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest))) = bits2bytes(uint2bits(i / 256)) + bits2bytes(int2bits(i % 256)).last '

Rule argument

name: bits2bytes-rec rotate: F subst: [bits] → [uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest]

Additional information

Used terms: uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest