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Proof step 18 from proof no-leading-zero (previous step)

int2bytes(bytes2int(i2b(0) ' + by ' + bytes1 + by0 ')) = i2b(0) ' + by ' + bytes1 + by0 ', 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → 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 19:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)
Proof step 20:
i2b(0) ' + by ' + bytes1 ≠ [], int2bytes(bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

Rule argument

name: bytes2int-rec rotate: F subst: [by, bytes] → [by0, i2b(0) ' + by ' + bytes1]

Additional information

Used simplifier rules: ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ by ' ≠ [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: by0, i2b(0) ' + by ' + bytes1