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Proof step 22 from proof int2bytes-rec-pos (previous step)

uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, 8 < # uint2bits(i / 256) + # fillsgn(9, uint2bits(i % 256)).rest, 0 ≤ i, 0 < i, 255 < i ⊦ bits2bytes(firstn(# uint2bits(i / 256) + # fillsgn(9, uint2bits(i % 256)).rest - 8, uint2bits(i))) + i2b(bits2int(lastn(8, uint2bits(i)))) ' = bits2bytes(uint2bits(i / 256)) + bits2bytes(int2bits(i % 256)).last '

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → # bits.rest = (# bits)-1 subst: [bits] → [fillsgn(9, uint2bits(i % 256))] rotate: F spec: list-data inst: bitlista name: length-rest

Additional information

Used simplifier rules: ⊦ fillsgn(n, bits) = [] ↔ bits = [] ∧ n = 0;% ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i % j;%0 ≤ i ⊦ uint2bits(i) ≠ []; Used terms: fillsgn(9, uint2bits(i % 256))