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Proof step 408 from proof bitsand-cast (previous step)

sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ bits3 + bits1 = [], bits1 = [], bits2 + mklist(true, m) = [], bits3 = [], lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits3, bits2 + mklist(true, m)) + bitsand(bits1, true ' + false ' + bits)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 409:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 410:
bits3 ≠ [] ∧ bits2 + mklist(true, m) ≠ [], sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ bits3 + bits1 = [], bits1 = [], bits2 + mklist(true, m) = [], bits3 = [], lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits2 + mklist(true, m), bits3) + bitsand(bits1, true ' + false ' + bits)))

Rule argument

name: and-com rotate: F subst: [bits0, bits] → [bits2 + mklist(true, m), bits3]

Additional information

Used terms: bits2 + mklist(true, m), bits3