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Proof step 118 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 119:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = fillsgn(# bits, bits0)
Proof step 120:
¬(¬ false ∈ mklist(true, m) ∧ # bits2 ≤ # mklist(true, m) ∧ bits2.first ∧ bits2 ≠ []), # bits = 2 + # bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, # bits2 < m, 2 + # bits1 + m < n ⊦ bits2 = [], bits = [], bits2 + bits = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(true, m), bits2) + bitsand(bits, true ' + false ' + bits1)))
Proof step 123:
¬ false ∈ mklist(true, m) ∧ # bits2 ≤ # mklist(true, m) ∧ bits2.first ∧ bits2 ≠ [], # bits = 2 + # bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, # bits2 < m, 2 + # bits1 + m < n ⊦ bits2 = [], bits = [], bits2 + bits = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, fillsgn(# mklist(true, m), bits2) + bitsand(bits, true ' + false ' + bits1)))

Rule argument

name: add-ones-grlen rotate: F subst: [bits0, bits] → [bits2, mklist(true, m)]

Additional information

Used terms: bits2, mklist(true, m)