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Proof step 4 from proof bits2bytes-app (previous step)

# bits0 % 8 = 0, ∀ bits1, bits2. # bits2 + # bits1 < # bits + # bits0 → # bits1 % 8 = 0 → bits2 = [] ∨ bits1 = [] ∨ bits2bytes(bits2 + bits1) = bits2bytes(bits2) + bits2bytes(bits1) ⊦ bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0), bits0 = [], bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 8 < # bits → bits2bytes(bits) = bits2bytes(firstn(# bits - 8, bits)) + i2b(bits2int(lastn(8, bits)))
Proof step 6:
¬ 8 < #(bits + bits0), # bits0 % 8 = 0, ∀ bits1, bits2. # bits2 + # bits1 < # bits + # bits0 → # bits1 % 8 = 0 → bits2 = [] ∨ bits1 = [] ∨ bits2bytes(bits2 + bits1) = bits2bytes(bits2) + bits2bytes(bits1) ⊦ bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0), bits0 = [], bits = []
Proof step 22:
8 < #(bits + bits0), # bits0 % 8 = 0, ∀ bits1, bits2. # bits2 + # bits1 < # bits + # bits0 → # bits1 % 8 = 0 → bits2 = [] ∨ bits1 = [] ∨ bits2bytes(bits2 + bits1) = bits2bytes(bits2) + bits2bytes(bits1) ⊦ bits2bytes(firstn(#(bits + bits0) - 8, bits + bits0)) + i2b(bits2int(lastn(8, bits + bits0))) = bits2bytes(bits) + bits2bytes(bits0), bits0 = [], bits = []

Rule argument

name: bits2bytes-rec rotate: F subst: [bits] → [bits + bits0]

Additional information

Used terms: bits + bits0