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Proof step 832 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 833:
⊦ ¬ true ∈ bits ∧ (# bits ≤ # bits0 ∨ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits

Rule argument

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

Additional information

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