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Proof step 412 from proof bitsand-cast (previous step)

# bits3 ≤ m, # bits1 = 2 + # bits, sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits ⊦ bits3 = [], bits2 + mklist(true, m) = [], lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits2 + mklist(true, m), bits3) + bitsand(bits1, true ' + false ' + bits))), bits1 = [], bits3 + bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 413:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ ¬ bits1.first → bitsand(bits + bits0, bits1) = bitsand(bits0, bits1)
Proof step 414:
¬(# bits3 ≤ # mklist(true, m) ∧ bits3 ≠ [] ∧ ¬ bits3.first), # bits3 ≤ m, # bits1 = 2 + # bits, sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits ⊦ bits3 = [], bits2 + mklist(true, m) = [], lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits2 + mklist(true, m), bits3) + bitsand(bits1, true ' + false ' + bits))), bits1 = [], bits3 + bits1 = []
Proof step 462:
# bits3 ≤ # mklist(true, m) ∧ bits3 ≠ [] ∧ ¬ bits3.first, # bits3 ≤ m, # bits1 = 2 + # bits, sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits ⊦ bits3 = [], bits2 + mklist(true, m) = [], lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(mklist(true, m), bits3) + bitsand(bits1, true ' + false ' + bits))), bits1 = [], bits3 + bits1 = []

Rule argument

name: bitsand-app-false rotate: F subst: [bits1, bits0, bits] → [bits3, mklist(true, m), bits2]

Additional information

Used terms: bits3, mklist(true, m), bits2