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Proof step 823 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 824:
⊦ ¬ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits0
Proof step 825:
¬(¬ mklist(false, # bits0).first ∧ # mklist(false, # bits0) ≤ # bits0 ∧ mklist(false, # bits0) ≠ []), sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits + # bits0 < # bitsand(bits0, mklist(false, # bits0)) + # bits1, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(bits0, mklist(false, # bits0)) + # bits1 ⊦ bits0 = [], 2 + # bits + # bits0 = # bitsand(bits0, mklist(false, # bits0)) + # bits1, (bits4 + bits0) + bits1 = [], bits4 + bits0 = [], bits2 + mklist(false, # bits0) = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, bitsand(bits0, mklist(false, # bits0)) + bitsand(bits1, false ' + true ' + bits)), bits2 = [], bits4 = [], bits1 = []

Rule argument

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

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: mklist(false, # bits0), bits0