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Proof step 4 from proof int2bytes-rec-pos (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 5:
0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = uint2bits(j / 2 ^ i) + fillsgn(i→n(i + 1), uint2bits(j % 2 ^ i)).rest
Proof step 6:
uint2bits(i) = uint2bits(i / 2 ^ 8) + fillsgn(i→n(8 + 1), uint2bits(i % 2 ^ 8)).rest, 0 ≤ i, 255 < i, 0 < i, 0 ≤ i ⊦ bits2bytes(uint2bits(i)) = bits2bytes(int2bits(i / 256)) + bits2bytes(int2bits(i % 256)).last '

Rule argument

seq: 0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = uint2bits(j / 2 ^ i) + fillsgn(i→n(i + 1), uint2bits(j % 2 ^ i)).rest subst: [i, j] → [8, i] rotate: F spec: int2bits inst: name: uint2bits-2potrec

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) Used terms: 8, i