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Proof step 80 from proof rightshift-8-01-01 (previous step)

i→n(j) < # int2bytes(i), 0 ≤ i ⊦ j = 0, bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i))) = 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 81:
⊦ # bytes ≤ n → firstn(n, bytes + bytes0) = bytes + firstn(n - # bytes, bytes0)
Proof step 82:
# mklist(i2b(0), i→n(j)) ≤ # int2bytes(i), i→n(j) < # int2bytes(i), 0 ≤ i ⊦ j = 0, bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i))) = bytes2int(mklist(i2b(0), i→n(j)) + firstn(# int2bytes(i) - # mklist(i2b(0), i→n(j)), int2bytes(i)))

Rule argument

seq: ⊦ # bytes ≤ n → firstn(n, bytes + bytes0) = bytes + firstn(n - # bytes, bytes0) subst: [bytes0, bytes, n] → [int2bytes(i), mklist(i2b(0), i→n(j)), # int2bytes(i)] rotate: F spec: list-del inst: bytelist name: firstn-app-01

Additional information

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