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Proof step 483 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 484:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 485:
bits0 ≠ [] ∧ mklist(true, # bits0) ≠ [], sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, mklist(true, # bits0).first ⊦ bits4 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bitsand(mklist(true, # bits0), bits0)) + bitsand(bits1, true ' + false ' + bits))), bits0 = [], bits4 + bits0 = []

Rule argument

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

Additional information

Used simplifier rules: ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ # bits = 0 ↔ bits = []; Used terms: mklist(true, # bits0), bits0