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Proof step 5 from proof bytes2bytes-first-neg (previous step)

∀ by, bytes0. # bytes0 < # bytes → true → (b2i(int2bytes(bytes2int(by ' + bytes0)).first) < 0 ↔ ¬ 0 ≤ b2i(by)) ⊦ bytes = [], b2i(int2bytes(bytes2int(by ' + bytes)).first) < 0 ↔ ¬ 0 ≤ b2i(by)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
bytes ≠ [], b2i(bytes.first) ≠ 0, b2i(bytes.first) ≠ ~1 ⊦ int2bytes(bytes2int(bytes)) = bytes
Proof step 7:
¬(by ' + bytes ≠ [] ∧ b2i((by ' + bytes).first) ≠ 0 ∧ b2i((by ' + bytes).first) ≠ ~1), ∀ by, bytes0. # bytes0 < # bytes → true → (b2i(int2bytes(bytes2int(by ' + bytes0)).first) < 0 ↔ ¬ 0 ≤ b2i(by)) ⊦ bytes = [], b2i(int2bytes(bytes2int(by ' + bytes)).first) < 0 ↔ ¬ 0 ≤ b2i(by)

Rule argument

name: bytes2bytes-other rotate: F subst: [bytes] → [by ' + bytes]

Additional information

Used simplifier rules: ⊦ (by ' + bytes).first = by;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: by ' + bytes