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Proof step 727 from proof bitsand-cast (previous step)

# bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits ⊦ mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, bitsand(bits2 + mklist(false, # bits0), bits4 + bits0) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits2 + mklist(false, # bits0) = [], bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits4 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 728:
⊦ # bits = # bits1 ∧ bits0 ≠ [] ∧ bits2 ≠ [] ∧ bits ≠ [] → bitsand(bits0 + bits, bits2 + bits1) = bitsand(bits0, bits2) + bitsand(bits, bits1)
Proof step 729:
¬(# mklist(false, # bits0) = # bits0 ∧ bits2 ≠ [] ∧ bits4 ≠ [] ∧ mklist(false, # bits0) ≠ []), # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits ⊦ mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, bitsand(bits2 + mklist(false, # bits0), bits4 + bits0) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits2 + mklist(false, # bits0) = [], bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits4 = []
Proof step 781:
# mklist(false, # bits0) = # bits0 ∧ bits2 ≠ [] ∧ bits4 ≠ [] ∧ mklist(false, # bits0) ≠ [], # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits ⊦ mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bitsand(bits2, bits4) + bitsand(mklist(false, # bits0), bits0)) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits2 + mklist(false, # bits0) = [], bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits4 = []

Rule argument

name: bitsand-app rotate: F subst: [bits1, bits2, bits, bits0] → [bits0, bits4, mklist(false, # bits0), bits2]

Additional information

Used terms: bits0, bits4, mklist(false, # bits0), bits2