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Proof step 47 from proof bytes2int-append (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
bytes2bits(bytes).first, bits2int(bytes2bits(bytes0)) < 0 ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bitsinvert(bytes2bits(bytes)) + bitsinvert(bytes2bits(bytes0)) = [], (bits2int(bytes2bits(bytes0)) + 1) % 2 ^ (8 * n→i(# bytes0)) = bits2int(bytes2bits(bytes0)) + 1

Rule argument

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = [];% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)%bits ≠ [] ⊦ bits2int(bits) < 0 → bits.first;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ n→i(n);% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i * j = j * i;