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Proof step 10 from proof no-leading-zero (previous step)

int2bytes(bytes2int(i2b(0) ' + by ')) = i2b(0) ' + by ', 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < # [] → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)
Proof step 12:
i2b(0) ' ≠ [], int2bytes(bytes2int(i2b(0) ') * 256 + band(b2i(by), 255)) = i2b(0) ' + by ', 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < # [] → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

Rule argument

name: bytes2int-rec rotate: F subst: [by, bytes] → [by, i2b(0) ']

Additional information

Used simplifier rules: ⊦ by ' ≠ []; Used terms: by, i2b(0) '