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Proof step 24 from proof fix-bits2bytes (previous step)

# bits % 8 = 0, # bits ≤ 8 * (n - 1), n ≤ # bits / 8 ⊦ bits = [], fix(n, bits2bytes(bits)) = bits2bytes(fillsgn(n * 8, bits)), n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [8, # bits] rotate: F spec: nat-div inst: name: modex

Additional information

Used simplifier rules: n ≠ 0 ⊦ (m * n) / n = m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;%0 ≠ m ⊦ (* m) * n ≤ m * n0 ↔ n ≤ n0;% ⊦ m < 1 ↔ m = 0;% ⊦ ¬ m ≤ n ↔ n < m;%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ m ≤ n → (n < m ↔ false);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: 8, # bits