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Proof step 2 from proof bytes2bits-length (previous step)

⊦ # bytes2bits(bytes) = # bytes * 8

User applied rule structural induction

And closed the goal!

Rule argument

indvar: bytes

Additional information

Used simplifier rules: bytes2bits-empty: ⊦ bytes2bits([]) = [];%bytes2bits-append: ⊦ bytes2bits(bytes + bytes0) = bytes2bits(bytes) + bytes2bits(bytes0);%bytes2bits-one: ⊦ bytes2bits(by ') = byte2bits(by);%byte2bits-length: ⊦ # byte2bits(by) = 8;%bytelist freely generated by [], +;;% ⊦ # [] = 0;% ⊦ # [] = 0;% ⊦ m * n = n * m;% ⊦ by + bytes = by ' + bytes;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bytes + bytes0) = # bytes + # bytes0;% ⊦ # by ' = 0 +1;% ⊦ m * (n + 1) = m * n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m + n = m + n0 ↔ n = n0;