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Proof step 576 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 577:
⊦ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits

Rule argument

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

Additional information

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