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Proof step 134 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 135:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 136:
n ≠ # fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), n = # fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)), # bits = 2 + # bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, bits2.first, # bits2 < m, 2 + # bits1 + m < n ⊦ bits2 = [], bits = [], bits2 + bits = [], fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)) = lastn(n, fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)))
Proof step 145:
n = # fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), n = # fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)), # bits = 2 + # bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, bits2.first, # bits2 < m, 2 + # bits1 + m < n ⊦ bits2 = [], bits = [], bits2 + bits = [], fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)) = fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [fillsgn (n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), n] rotate: F spec: list-del inst: bitlista name: lastN-all

Additional information

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