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Proof step 12 from proof rightshift-8-01-01 (previous step)

# int2bytes(i) ≤ i→n(j), # int2bytes(i) ≤ i→n(j), 0 ≤ i ⊦ j = 0, i >> 8 * j = bytes2int(firstn(# int2bytes(i), mklist(i2b(0), i→n(j)) + int2bytes(i)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ m ≤ # bytes → firstn(m, bytes + bytes0) = firstn(m, bytes)
Proof step 14:
# int2bytes(i) ≤ # mklist(i2b(0), i→n(j)), # int2bytes(i) ≤ i→n(j), # int2bytes(i) ≤ i→n(j), 0 ≤ i ⊦ j = 0, i >> 8 * j = bytes2int(firstn(# int2bytes(i), mklist(i2b(0), i→n(j))))

Rule argument

seq: ⊦ m ≤ # bytes → firstn(m, bytes + bytes0) = firstn(m, bytes) subst: [bytes0, bytes, m] → [int2bytes(i), mklist(i2b(0), i→n(j)), # int2bytes(i)] rotate: F spec: list-del inst: bytelist name: first-append

Additional information

Used simplifier rules: ⊦ # mklist(by, n) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m ≤ n → (n < m ↔ false); Used terms: int2bytes(i), mklist(i2b(0), i→n(j)), # int2bytes(i)