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Proof step 732 from proof bitsand-cast (previous step)

# bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits ⊦ bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits4 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, bitsand(mklist(false, # bits0), bits4 + bits0) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 733:
⊦ ¬ true ∈ bits ∧ (# bits ≤ # bits0 ∨ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits
Proof step 734:
¬ true ∈ mklist(false, # bits0) ∧ (# mklist(false, # bits0) ≤ #(bits4 + bits0) ∨ (bits4 + bits0).first) ∧ mklist(false, # bits0) ≠ [] ∧ bits4 + bits0 ≠ [], # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits ⊦ bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits4 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, mklist(false, # bits0) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits0 = []

Rule argument

name: bitsand-zeros rotate: F subst: [bits0, bits] → [bits4 + bits0, mklist(false, # bits0)]

Additional information

Used simplifier rules: ⊦ ¬ true ∈ mklist(false, n);% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ # bits = 0 ↔ bits = []; Used terms: bits4 + bits0, mklist(false, # bits0)