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Proof step 7 from proof rightshift-8-02 (previous step)

# int2bytes(i) = 1, 0 ≤ i ⊦ i >> 8 = bytes2int(fillsgn(2, int2bytes(i)).butlast)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ # bytes < n ∧ 0 ≤ bytes2int(bytes) → fillsgn(n, bytes) = mklist(i2b(0), n - # bytes) + bytes
Proof step 9:
# int2bytes(i) < 2 ∧ 0 ≤ bytes2int(int2bytes(i)), # int2bytes(i) = 1, 0 ≤ i ⊦ i >> 8 = bytes2int((mklist(i2b(0), 2 - # int2bytes(i)) + int2bytes(i)).butlast)

Rule argument

name: fillsgn-pos rotate: F subst: [bytes, n] → [int2bytes(i), 2]

Additional information

Used simplifier rules: int2int: ⊦ bytes2int(int2bytes(i)) = i;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);%0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) Used terms: int2bytes(i), 2