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Proof step 86 from proof bytes2int-append (previous step)

bits2int(bytes2bits(bytes0)) < 0 ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes0)) = band(bits2int(bytes2bits(bytes0)), 2 ^ (8 * n→i(# bytes0)) - 1), bytes2bits(bytes).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 87:
⊦ j < 0 ∧ 0 ≤ i → band(j, 2 ^ i - 1) = (j + 1) % 2 ^ i + 2 ^ i - 1
Proof step 88:
bits2int(bytes2bits(bytes0)) < 0 ∧ 0 ≤ 8 * n→i(# bytes0), bits2int(bytes2bits(bytes0)) < 0 ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes0)) = (bits2int(bytes2bits(bytes0)) + 1) % 2 ^ (8 * n→i(# bytes0)) + 2 ^ (8 * n→i(# bytes0)) - 1, bytes2bits(bytes).first

Rule argument

seq: ⊦ j < 0 ∧ 0 ≤ i → band(j, 2 ^ i - 1) = (j + 1) % 2 ^ i + 2 ^ i - 1 subst: [i, j] → [8 * n→i(# bytes0), bits2int(bytes2bits(bytes0))] rotate: F spec: intops inst: name: band-011x-neg

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ 0 ≤ n→i(n);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: 8 * n→i(# bytes0), bits2int(bytes2bits(bytes0))