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Proof step 17 from proof bits2bytes-fill (previous step)

((8 - # bits % 8) + # bits) % 8 = 0, 8 < (8 - # bits % 8) + # bits ⊦ bits = [], # bits % 8 = 0, bits2bytes(bits) = bits2bytes(firstn(8, mklist(bits.first, 8 - # bits % 8) + bits)) + bits2bytes(restn(8, mklist(bits.first, 8 - # bits % 8) + bits)), 8 + # bits = # bits % 8

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ m ≤ # bits + # bits0 ∧ # bits ≤ m → restn(m, bits + bits0) = restn(m - # bits, bits0)
Proof step 19:
8 ≤ # mklist(bits.first, 8 - # bits % 8) + # bits ∧ # mklist(bits.first, 8 - # bits % 8) ≤ 8, ((8 - # bits % 8) + # bits) % 8 = 0, 8 < (8 - # bits % 8) + # bits ⊦ bits = [], # bits % 8 = 0, bits2bytes(bits) = bits2bytes(firstn(8, mklist(bits.first, 8 - # bits % 8) + bits)) + bits2bytes(restn(8 - # mklist(bits.first, 8 - # bits % 8), bits)), 8 + # bits = # bits % 8

Rule argument

seq: ⊦ m ≤ # bits + # bits0 ∧ # bits ≤ m → restn(m, bits + bits0) = restn(m - # bits, bits0) subst: [bits0, bits, m] → [bits, mklist(bits.first, 8 - # bits % 8), 8] rotate: F spec: list-del inst: bitlista name: rest-app

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m + n = n + m;% ⊦ m < n → ¬ n < m;%n ≠ 0 ⊦ m % n ≤ n;%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1; Used terms: bits, mklist(bits.first, 8 - # bits % 8), 8