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Proof step 4 from proof bytes2int-mklist-zeros-01 (previous step)

0 ≤ b2i(bytes.first), ∀ n, bytes0. # bytes0 < # bytes → 0 ≤ b2i(bytes0.first) → bytes2int(mklist(i2b(0), n) + bytes0) = bytes2int(bytes0) ∨ bytes0 = [] ⊦ bytes = [], bytes2int(mklist(i2b(0), n) + bytes) = bytes2int(bytes)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 1 < # bytes → bytes2int(bytes) = bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)
Proof step 6:
¬ 1 < # bytes, 0 ≤ b2i(bytes.first), ∀ n, bytes0. # bytes0 < # bytes → 0 ≤ b2i(bytes0.first) → bytes2int(mklist(i2b(0), n) + bytes0) = bytes2int(bytes0) ∨ bytes0 = [] ⊦ bytes = [], bytes2int(mklist(i2b(0), n) + bytes) = bytes2int(bytes)
Proof step 11:
1 < # bytes, 0 ≤ b2i(bytes.first), ∀ n, bytes0. # bytes0 < # bytes → 0 ≤ b2i(bytes0.first) → bytes2int(mklist(i2b(0), n) + bytes0) = bytes2int(bytes0) ∨ bytes0 = [] ⊦ bytes = [], bytes2int(mklist(i2b(0), n) + bytes) = bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)

Rule argument

name: bytes2int-rec-01 rotate: F subst: [bytes] → [bytes]

Additional information

Used terms: bytes