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Proof step 434 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, 2 + # bits + n = n0 + # bits1, bits3.first ⊦ bits1 = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(true, n) + mklist(true, # bits3) = [], bits3 + bitsand(bits1, true ' + false ' + bits) = [], lastn(2 + # bits + n + # bits3, mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits)) = lastn(2 + # bits + n + # bits3, fillsgn(2 + # bits + n + # bits3, bits2 + mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 435:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 436:
2 + # bits + n + # bits3 ≠ #(mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits)), # bits1 = 2 + # bits, sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, 2 + # bits + n = n0 + # bits1, bits3.first ⊦ bits1 = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(true, n) + mklist(true, # bits3) = [], bits3 + bitsand(bits1, true ' + false ' + bits) = [], lastn(2 + # bits + n + # bits3, mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits)) = lastn(2 + # bits + n + # bits3, fillsgn(2 + # bits + n + # bits3, bits2 + mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits)))
Proof step 439:
2 + # bits + n + # bits3 = #(mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits)), # bits1 = 2 + # bits, sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, 2 + # bits + n = n0 + # bits1, bits3.first ⊦ bits1 = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(true, n) + mklist(true, # bits3) = [], bits3 + bitsand(bits1, true ' + false ' + bits) = [], mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits) = lastn(2 + # bits + n + # bits3, fillsgn(2 + # bits + n + # bits3, bits2 + mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits)))

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [ mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits), 2 + # bits + n + # bits3] rotate: F spec: list-del inst: bitlista name: lastN-all

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits), 2 + # bits + n + # bits3