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Proof step 12 from proof bytes2int-rec-first-zero (previous step)

∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → bytes0 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes0) = band(b2i(by), 255) * 256 ^ n→i(# bytes0) + bytes2int(i2b(0) ' + bytes0) ⊦ 256 * bytes2int((i2b(0) ' + by ') + bytes1) = bytes2int(i2b(0) ' + bytes1) * 256 + 256 ^ (n→i(# bytes1) + 1) * band(b2i(by), 255)

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [by, bytes0] → [by, bytes1]

Additional information

Used simplifier rules: ⊦ #(bytes + bytes0) = # bytes + # bytes0;% ⊦ # by ' = 0 +1;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ ¬ n < n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: by, bytes1