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Proof step 530 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 531:
⊦ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits
Proof step 532:
¬(mklist(true, # bits0).first ∧ # mklist(true, # bits0) ≤ # bits0 ∧ mklist(true, # bits0) ≠ []), # bits1 = 2 + # bits, sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(bits0, mklist(true, # bits0)) + # bits1 ⊦ bits4 + bits0 = [], bits2 + mklist(true, # bits0) = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + # bits0, (bitsand(bits2, bits4) + bitsand(bits0, mklist(true, # bits0))) + bitsand(bits1, true ' + false ' + bits)), bits1 = [], (bits4 + bits0) + bits1 = [], bits2 = [], bits4 = [], bits0 = []
Proof step 535:
mklist(true, # bits0).first ∧ # mklist(true, # bits0) ≤ # bits0 ∧ mklist(true, # bits0) ≠ [], # bits1 = 2 + # bits, sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bits0 + # bits1 ⊦ bits4 + bits0 = [], bits2 + mklist(true, # bits0) = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + # bits0, (bitsand(bits2, bits4) + bitsand(bits0, mklist(true, # bits0))) + bitsand(bits1, true ' + false ' + bits)), bits1 = [], (bits4 + bits0) + bits1 = [], bits2 = [], bits4 = [], bits0 = []

Rule argument

name: bitsand-len-true rotate: F subst: [bits0, bits] → [mklist(true, # bits0), bits0]

Additional information

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