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Proof step 664 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 665:
⊦ ¬ true ∈ bits ∧ (# bits0 < # bits ∧ ¬ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = mklist(false, # bits0)
Proof step 666:
¬ true ∈ mklist(false, m) ∧ # bits3 < # mklist(false, m) ∧ ¬ bits3.first ∧ mklist(false, m) ≠ [] ∧ bits3 ≠ [], # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, # bits3 < m ⊦ # bits3 = m, bits3 = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3.first

Rule argument

name: bitsand-zeros-01 rotate: F subst: [bits0, bits] → [bits3, mklist(false, m)]

Additional information

Used simplifier rules: ⊦ ¬ true ∈ mklist(false, n);% ⊦ # mklist(boolvar, n) = n;% ⊦ m ≠ n → (¬ m < n ↔ n < m);% ⊦ m < n → ¬ n < m;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ m < n → n ≠ 0; Used terms: bits3, mklist(false, m)