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Proof step 449 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) = [], mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits) = lastn(2 + # bits + n + # bits3, mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 450:
⊦ # bits ≤ n → lastn(n, bits0 + bits) = lastn(n - # bits, bits0) + bits
Proof step 451:
¬ #(bits3 + bitsand(bits1, true ' + false ' + bits)) ≤ 2 + # bits + n + # bits3, # 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, mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits))
Proof step 454:
#(bits3 + bitsand(bits1, true ' + false ' + bits)) ≤ 2 + # bits + n + # bits3, # 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 - #(bits3 + bitsand(bits1, true ' + false ' + bits)), mklist(true, n)) + bits3 + bitsand(bits1, true ' + false ' + bits)

Rule argument

seq: ⊦ # bits ≤ n → lastn(n, bits0 + bits) = lastn(n - # bits, bits0) + bits subst: [bits, bits0, n] → [bits3 + bitsand(bits1, true ' + false ' + bits), mklist(true, n), 2 + # bits + n + # bits3] rotate: F spec: list-del inst: bitlista name: lastn-app

Additional information

Used terms: bits3 + bitsand(bits1, true ' + false ' + bits), mklist(true, n), 2 + # bits + n + # bits3