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Proof step 20 from proof bits2bytes-rec-02 (previous step)

# bits = 16, ∀ bits0. # bits0 < 16 → true → # bits0 % 8 = 0 ∧ 8 < # bits0 → bits2bytes(bits0) = bits2bytes(firstn(8, bits0)) + bits2bytes(restn(8, bits0)) ⊦ bits2int(lastn(8, bits)) = bits2int(restn(8, bits)), i2b(bits2int(lastn(8, bits))) = i2b(bits2int(restn(8, bits))), bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
n ≤ # bits ⊦ lastn(n, bits) = restn(# bits - n, bits)

Rule argument

seq: n ≤ # bits ⊦ lastn(n, bits) = restn(# bits - n, bits) subst: [bits, n] → [bits, 8] rotate: F spec: list-del inst: bitlista name: lastN-restN

Additional information

Used simplifier rules: ⊦ i2b(i) ≠ i2b(j) → i ≠ j; (forward)% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n → n ≠ 0; (forward) Used terms: bits, 8