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Proof step 127 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 128:
⊦ # bits ≤ n → # fillsgn(n, bits) = n
Proof step 129:
¬ #(bits2 + bitsand(bits, true ' + false ' + bits1)) ≤ n, sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), # bits = 2 + # bits1, 2 + # bits1 + m < n, # bits2 < m, bits2.first ⊦ n = # fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)), lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))), bits2 + bits = [], bits = [], bits2 = []

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [bits2 + bitsand(bits, true ' + false ' + bits1), n] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used terms: bits2 + bitsand(bits, true ' + false ' + bits1), n