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Proof step 20 from proof int2bytes-fillsgn-rec (previous step)

bytes2int(int2bytes(i >> 8) + i2b(i) ') < 0, # int2bytes(i >> 8) + 1 < n, 0 ≤ i, 0 < i, 0 ≤ i >> 8, 128 ≤ i, # int2bytes(i >> 8) < n ⊦ n = # int2bytes(i >> 8) + 1, fillsgn(n, int2bytes(i >> 8) + i2b(i) ') = (mklist(i2b(0), n - 1 - # int2bytes(i >> 8)) + int2bytes(i >> 8)) + i2b(i) '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ bytes ≠ [] → (bytes2int(bytes) < 0 ↔ b2i(bytes.first) < 0)
Proof step 22:
int2bytes(i >> 8) + i2b(i) ' ≠ [], b2i((int2bytes(i >> 8) + i2b(i) ').first) < 0, # int2bytes(i >> 8) + 1 < n, 0 ≤ i, 0 < i, 0 ≤ i >> 8, 128 ≤ i, # int2bytes(i >> 8) < n ⊦ n = # int2bytes(i >> 8) + 1, fillsgn(n, int2bytes(i >> 8) + i2b(i) ') = (mklist(i2b(0), n - 1 - # int2bytes(i >> 8)) + int2bytes(i >> 8)) + i2b(i) '

Rule argument

name: bytes2int-neg rotate: F subst: [bytes] → [int2bytes(i >> 8) + i2b(i) ']

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ [];% ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: int2bytes(i >> 8) + i2b(i) '