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Proof step 17 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)) ⊦ bits = [], i2b(bits2int(lastn(8, bits))) ' = bits2bytes(restn(8, bits))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ # bits ≤ 8 → bits2bytes(bits) = i2b(bits2int(bits)) '
Proof step 19:
# restn(8, bits) ≤ 8, # bits = 16, ∀ bits0. # bits0 < 16 → true → # bits0 % 8 = 0 ∧ 8 < # bits0 → bits2bytes(bits0) = bits2bytes(firstn(8, bits0)) + bits2bytes(restn(8, bits0)) ⊦ bits = [], i2b(bits2int(lastn(8, bits))) ' = i2b(bits2int(restn(8, bits))) '

Rule argument

name: bits2bytes-base rotate: F subst: [bits] → [restn(8, bits)]

Additional information

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