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Proof step 7 from proof bytes2int-first-pos (previous step)

band(255, b2i(bytes.last)) + 256 * bytes2int(by ' + bytes.butlast) < 0, 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < # bytes → bytes2int(by ' + bytes0) < 0 ∧ 0 ≤ b2i(by) → false ⊦ bytes = []

User applied rule apply induction

And obtained the following new goals

Proof step 8:
band(255, b2i(bytes.last)) + 256 * bytes2int(by ' + bytes.butlast) < 0, 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < # bytes → bytes2int(by ' + bytes0) < 0 ∧ 0 ≤ b2i(by) → false ⊦ bytes2int(by ' + bytes.butlast) < 0 ∧ 0 ≤ b2i(by), bytes = []

Rule argument

subst: [by, bytes0] → [by, bytes.butlast]

Additional information

Used simplifier rules: ⊦ bytes ≠ [] → # bytes.butlast = # bytes - 1;% ⊦ # bytes = 0 ↔ bytes = [];% ⊦ m < 1 ↔ m = 0;% ⊦ ¬ m ≤ n ↔ n < m;%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ ¬ n < n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: by, bytes.butlast