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Proof step 16 from proof band-011x-is-lastn (previous step)

# bits = i→n(i) + 1, int2bits(j) = bits0 + bits, i→n(i) < # bits, 0 < i, i→n(i) < # bits0 + # bits ⊦ bits2int(bitsand(bits, false ' + mklist(true, i→n(i)))) = bits2uint(lastn(i→n(i), bits0 + bits)), i→n(i) = # bits0 + # bits, bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits)
Proof step 18:
i→n(i) ≤ # bits, # bits = i→n(i) + 1, int2bits(j) = bits0 + bits, i→n(i) < # bits, 0 < i, i→n(i) < # bits0 + # bits ⊦ bits2int(bitsand(bits, false ' + mklist(true, i→n(i)))) = bits2uint(lastn(i→n(i), bits)), i→n(i) = # bits0 + # bits, bits = []

Rule argument

seq: ⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits) subst: [bits, bits0, n] → [bits, bits0, i→n(i)] rotate: F spec: list-del inst: bitlista name: lastN-append-01

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: bits, bits0, i→n(i)