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Proof step 17 from proof int2bytes-bytes2int-length-01 (previous step)

# bytes ≤ # sgn(bytes2bits(bytes)) / 8, # sgn(bytes2bits(bytes)) ≤ 8 * # bytes ⊦ bytes = [], # sgn(bytes2bits(bytes)) % 8 = 0

User applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat-div inst: name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [# sgn(bytes2bits(bytes)), 8, m, n] flags: []

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%mod-nle-01: ⊦ n0 < m0 ∧ n ≤ m ∧ n0 ≠ 0 → ¬ m0 * m + n0 ≤ m0 * n; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: # sgn(bytes2bits(bytes)), 8, m, n