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Proof step 31 from proof bytes2bytes-first-neg (previous step)

0 ≤ b2i(int2bytes(bytes2int(i2b(~1) ' + by0 ' + bytes1)).first), b2i(by0) < 0, ∀ by, bytes0. # bytes0 < #(by0 + bytes1) → true → (b2i(int2bytes(bytes2int(by ' + bytes0)).first) < 0 ↔ ¬ 0 ≤ b2i(by)) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ b2i(by) < 0 → bytes2int(i2b(~1) ' + by ' + bytes) = bytes2int(by ' + bytes)
Proof step 33:
b2i(by0) < 0, 0 ≤ b2i(int2bytes(bytes2int(by0 ' + bytes1)).first), b2i(by0) < 0, ∀ by, bytes0. # bytes0 < #(by0 + bytes1) → true → (b2i(int2bytes(bytes2int(by ' + bytes0)).first) < 0 ↔ ¬ 0 ≤ b2i(by)) ⊦

Rule argument

name: bytes2int-mone rotate: F subst: [bytes, by] → [bytes1, by0]

Additional information

Used terms: bytes1, by0