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Proof step 561 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), # bits1 ≤ # bitsand(bits1, true ' + false ' + bits) ⊦ bits0 = [], bits4 = [], bits2 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, 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

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [bits0 + bitsand(bits1, true ' + false ' + bits), 2 + # bits + # bits0] 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: bits0 + bitsand(bits1, true ' + false ' + bits), 2 + # bits + # bits0