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Proof step 553 from proof bitsand-cast (previous step)

sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, mklist(true, # bits0).first, 2 + # bits + # bits0 ≤ # bitsand(bits0, mklist(true, # bits0)) + # bitsand(bits1, true ' + false ' + bits), # bits1 ≤ # bits4 + # bitsand(bits1, true ' + false ' + bits) ⊦ bits0 = [], bits4 = [], bits2 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, (bits4 + 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 554:
⊦ (bits + bits0) + bits1 = bits + bits0 + bits1
Proof step 555:
sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, mklist(true, # bits0).first, 2 + # bits + # bits0 ≤ # bitsand(bits0, mklist(true, # bits0)) + # bitsand(bits1, true ' + false ' + bits), # bits1 ≤ # bits4 + # bitsand(bits1, true ' + false ' + bits) ⊦ bits0 = [], bits4 = [], bits2 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, bits4 + 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 = []

Rule argument

seq: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1 subst: [bits1, bits0, bits] → [bitsand(bits1, true ' + false ' + bits), bits0, bits4] rotate: F spec: list inst: bitlista name: a

Additional information

Used terms: bitsand(bits1, true ' + false ' + bits), bits0, bits4