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Proof step 469 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 470:
⊦ # bits = # bits1 ∧ bits0 ≠ [] ∧ bits2 ≠ [] ∧ bits ≠ [] → bitsand(bits0 + bits, bits2 + bits1) = bitsand(bits0, bits2) + bitsand(bits, bits1)
Proof step 471:
¬(# mklist(true, # bits0) = # bits0 ∧ bits2 ≠ [] ∧ bits4 ≠ [] ∧ mklist(true, # bits0) ≠ []), sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, bitsand(bits2 + mklist(true, # bits0), bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))), bits2 + mklist(true, # bits0) = [], bits4 + bits0 = [], bits4 = []
Proof step 508:
# mklist(true, # bits0) = # bits0 ∧ bits2 ≠ [] ∧ bits4 ≠ [] ∧ mklist(true, # bits0) ≠ [], sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bitsand(bits2, bits4) + bitsand(mklist(true, # bits0), bits0)) + bitsand(bits1, true ' + false ' + bits))), bits2 + mklist(true, # bits0) = [], bits4 + bits0 = [], bits4 = []

Rule argument

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

Additional information

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