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Proof step 12 from proof bits2bytes-len (previous step)

# bits2bytes(firstn(# bits - 8, bits)) = 1 + (# bits - 8 - 1) / 8, 8 < # bits, ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ # bits2bytes(bits0) = (# bits0 - 1) / 8 + 1 ⊦ bits = [], 1 + (# bits - 8 - 1) / 8 = (# bits - 1) / 8

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: n ≠ 0 ⊦ n ≤ m → m / n = (m - n) / n + 1 subst: [n, m] → [8, # bits - 1] rotate: F spec: nat-div inst: name: rec

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ m < 1 ↔ m = 0;% ⊦ ¬ m ≤ n ↔ n < m;%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n;% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) Used terms: 8, # bits - 1