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Proof step 10 from proof bytes2int-neg (previous step)

∀ bytes0. # bytes0 < #(by + (bytes + by0 ')) → true → bytes0 ≠ [] → (bytes2int(bytes0) < 0 ↔ b2i(bytes0.first) < 0) ⊦ band(255, b2i(by0)) + 256 * bytes2int(by ' + bytes) < 0 ↔ ¬ 0 ≤ b2i(by)

User applied rule apply induction

And obtained the following new goals

Proof step 11:
by ' + bytes ≠ [] → (bytes2int(by ' + bytes) < 0 ↔ b2i((by ' + bytes).first) < 0), ∀ bytes0. # bytes0 < #(by + (bytes + by0 ')) → true → bytes0 ≠ [] → (bytes2int(bytes0) < 0 ↔ b2i(bytes0.first) < 0) ⊦ band(255, b2i(by0)) + 256 * bytes2int(by ' + bytes) < 0 ↔ ¬ 0 ≤ b2i(by)

Rule argument

subst: [bytes0] → [by ' + bytes]

Additional information

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