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Proof step 8 from proof int2bytes-rec255-neg (previous step)

# int2bytes(i % 256) < 2, i < 0, i < ~128 ⊦ fix(2, int2bytes(i % 256)).rest = int2bytes(i % 256).last '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ # bytes < n ∧ bytes2int(bytes) < 0 → fix(n, bytes) = mklist(i2b(~1), n - # bytes) + bytes
Proof step 10:
# int2bytes(i % 256) < 2 ∧ bytes2int(int2bytes(i % 256)) < 0, # int2bytes(i % 256) < 2, i < 0, i < ~128 ⊦ (mklist(i2b(~1), 2 - # int2bytes(i % 256)) + int2bytes(i % 256)).rest = int2bytes(i % 256).last '

Rule argument

name: fix-neg rotate: F subst: [bytes, n] → [int2bytes(i % 256), 2]

Additional information

Used simplifier rules: int2int: ⊦ bytes2int(int2bytes(i)) = i;%int2bytes-byte: ~128 ≤ i, i < 128 ⊦ int2bytes((* i)) = i2b(i) ';%fix-two: ⊦ fix(2, i2b(0) ') = i2b(0) ' + i2b(0) ';% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n → (n ≤ m ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < j ∧ i < 0 → (0 ≤ i % j ↔ i % j = 0);% ⊦ (by ' + bytes).rest = bytes;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ by '.last = by;% ⊦ by ' = by0 ' ↔ by = by0; Used terms: int2bytes(i % 256), 2