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Proof step 582 from proof bitsand-cast (previous step)

# bits1 = # bitsand(bits1, true ' + false ' + bits), # bits1 = 2 + # bits, sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, 2 + # bits + # bits0 = # bitsand(mklist(true, # bits0), bits0) + # bits1, mklist(true, # bits0).first ⊦ bits1 = [], (bits4 + bits0) + bits1 = [], bits2 = [], bits4 = [], bits0 = [], bits4 + bits0 = [], bits2 + mklist(true, # bits0) = [], bits0 = bitsand(mklist(true, # bits0), bits0), bits0.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 583:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ ¬ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits0

Rule argument

name: add-ones-grlen-02 rotate: F subst: [bits0, bits] → [bits0, mklist(true, # bits0)]

Additional information

Used simplifier rules: ⊦ ¬ false ∈ mklist(true, n);% ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ n < n; Used terms: bits0, mklist(true, # bits0)