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Proof step 707 from proof bitsand-cast (previous step)

# bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, # bits3 < m, 2 + # bits + m ≤ # bits3 + # bits1 ⊦ # bits3 = m, mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3 = [], bits1 = [], bits3.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 708:
⊦ # bits ≤ n → lastn(n, bits0 + bits) = lastn(n - # bits, bits0) + bits
Proof step 709:
# bitsand(bits1, false ' + true ' + bits) ≤ 2 + # bits + m, # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, # bits3 < m, 2 + # bits + m ≤ # bits3 + # bits1 ⊦ # bits3 = m, mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m - # bitsand(bits1, false ' + true ' + bits), mklist(false, # bits3)) + bitsand(bits1, false ' + true ' + bits), bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3 = [], bits1 = [], bits3.first

Rule argument

seq: ⊦ # bits ≤ n → lastn(n, bits0 + bits) = lastn(n - # bits, bits0) + bits subst: [bits, bits0, n] → [bitsand(bits1, false ' + true ' + bits), mklist(false, # bits3), 2 + # bits + m] rotate: F spec: list-del inst: bitlista name: lastn-app

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ ¬ m + n < m; Used terms: bitsand(bits1, false ' + true ' + bits), mklist(false, # bits3), 2 + # bits + m