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Proof step 29 from proof fill-lastn-03 (previous step)

# bits ≤ n, # bits ≤ m, m ≤ n ⊦ bits = [], restn(n - m, mklist(bits.first, n - # bits) + bits) = mklist(bits.first, m - # bits) + bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ n ≤ # bits → restn(n, bits + bits0) = restn(n, bits) + bits0
Proof step 31:
¬ n - m ≤ # mklist(bits.first, n - # bits), # bits ≤ n, # bits ≤ m, m ≤ n ⊦ bits = [], restn(n - m, mklist(bits.first, n - # bits) + bits) = mklist(bits.first, m - # bits) + bits
Proof step 33:
n - m ≤ # mklist(bits.first, n - # bits), # bits ≤ n, # bits ≤ m, m ≤ n ⊦ bits = [], restn(n - m, mklist(bits.first, n - # bits)) + bits = mklist(bits.first, m - # bits) + bits

Rule argument

seq: ⊦ n ≤ # bits → restn(n, bits + bits0) = restn(n, bits) + bits0 subst: [bits0, bits, n] → [bits, mklist(bits.first, n - # bits), n - m] rotate: F spec: list-del inst: bitlista name: restN-append

Additional information

Used terms: bits, mklist(bits.first, n - # bits), n - m