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Proof step 23 from proof bytes2int-fillsgn-zero (previous step)

# bytes = m + 1, n ≤ m, bytes[n] ∈ bytes → b2i(bytes[n]) = 0 ⊦ bytes = [], m = 0, (mklist(i2b(0), m) + i2b(0) ')[n] = bytes[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ m < # bytes → (¬ bytes[m] ∈ bytes ↔ false)
Proof step 25:
n < # bytes, # bytes = m + 1, n ≤ m, true → b2i(bytes[n]) = 0 ⊦ bytes = [], m = 0, (mklist(i2b(0), m) + i2b(0) ')[n] = bytes[n]

Rule argument

seq: ⊦ m < # bytes → (¬ bytes[m] ∈ bytes ↔ false) subst: [m, bytes] → [n, bytes] rotate: F spec: list-del inst: bytelist name: get-in

Additional information

Used simplifier rules: ⊦ ¬ m < n ↔ n ≤ m;% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m = n + 1 → ¬ m ≤ n;% ⊦ m + m0 ≤ m ↔ m0 = 0; Used terms: n, bytes