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Proof step 54 from proof int2bytes-rec-neg-05 (previous step)

# bits2bytes(restn(# int2bits(j) % 8, int2bits(j))) = i→n(i), j < 0, 0 < 2 ^ (i * 8) + j, 0 < j + 2 ^ (i * 8), j + 2 ^ (i * 8 - 1) < 0, 0 < i, 8 < # int2bits(j) ⊦ j = 0, # int2bits(j) % 8 = 0, i2b(bits2int(firstn(# int2bits(j) % 8, int2bits(j)))) = i2b(~1), bits2int(firstn(# int2bits(j) % 8, int2bits(j))) = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i, ~(2 ^ (i + 1)) ≤ j, j < ~(2 ^ i) ⊦ # int2bits(j) = i→n(i + 2) subst: [i, j] → [i * 8 - 1, j] rotate: F spec: int2bits inst: name: int2bits-len-neg

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + (j - i) = j;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i * 8 - 1, j