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Proof step 34 from proof bytes2bytes-length (previous step)

2 + # bytes < # int2bytes(bytes2int(by ' + bytes)), b2i(by) < 0, ∀ bytes0. # bytes0 < #(i2b(~1) + by + bytes) → # bytes0 < # int2bytes(bytes2int(bytes0)) → bytes0 = [] ⊦

User applied rule apply induction

And closed the goal!

Rule argument

subst: [bytes0] → [by ' + bytes]

Additional information

Used simplifier rules: ⊦ by ' ≠ [];% ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ by + bytes = by ' + bytes;% ⊦ #(bytes + bytes0) = # bytes + # bytes0;% ⊦ # by ' = 0 +1;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: by ' + bytes