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Proof step 18 from proof fill-lastn-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
n ≤ # bits ⊦ lastn(n, bits) = restn(# bits - n, bits)
Proof step 20:
m ≤ #(mklist(bits.first, n - # bits) + bits), # bits ≤ n, m ≤ n, # bits ≤ m ⊦ bits = [], restn(#(mklist(bits.first, n - # bits) + bits) - m, mklist(bits.first, n - # bits) + bits) = lastn(m, mklist(bits.first, m - # bits) + bits)

Rule argument

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

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n → n ≠ 0;% ⊦ ¬ n + (m - n) < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: mklist(bits.first, n - # bits) + bits, m