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Proof step 77 from proof rightshift-8-01-01 (previous step)

i→n(j) < # int2bytes(i), 0 ≤ i ⊦ bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i))) = bytes2int(firstn(# int2bytes(i), fillsgn(i→n(j) + # int2bytes(i), int2bytes(i)))), j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 78:
⊦ # bytes < n ∧ 0 ≤ bytes2int(bytes) → fillsgn(n, bytes) = mklist(i2b(0), n - # bytes) + bytes
Proof step 79:
# int2bytes(i) < i→n(j) + # int2bytes(i) ∧ 0 ≤ bytes2int(int2bytes(i)), i→n(j) < # int2bytes(i), 0 ≤ i ⊦ bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i))) = bytes2int(firstn(# int2bytes(i), mklist(i2b(0), i→n(j) + # int2bytes(i) - # int2bytes(i)) + int2bytes(i))), j = 0

Rule argument

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

Additional information

Used simplifier rules: int2int: ⊦ bytes2int(int2bytes(i)) = i;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m + m0 ≤ m ↔ m0 = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: int2bytes(i), i→n(j) + # int2bytes(i)