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Proof step 62 from proof no-leading-zero (previous step)

int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) % 256).last = by0, int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) / 256) = i2b(0) ' + by ' + bytes1, bytes2int(i2b(0) ' + by ' + bytes1) < 0, 0 < bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255), 0 ≤ b2i(by), 255 < bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255), ∀ 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 63:
⊦ bytes ≠ [] → (bytes2int(bytes) < 0 ↔ b2i(bytes.first) < 0)

Rule argument

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

Additional information

Used simplifier rules: ⊦ by ' ≠ [];% ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ by ' + bytes ≠ [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ (by ' + bytes).first = by;% ⊦ b2i(i2b(0)) = 0; Used terms: i2b(0) ' + by ' + bytes1