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Proof step 585 from proof bitsand-cast (previous step)

sgn(mklist(false, n - 1) + false ' + true ' + bits) = false ' + true ' + bits, # bits1 = 2 + # bits ⊦ n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits1, false ' + true ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(false, n - 1)) + false ' + true ' + bits, bits3 + bits1))), bits3 = [], bits3 + bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 586:
⊦ # bits = # bits1 ∧ bits0 ≠ [] ∧ bits2 ≠ [] ∧ bits ≠ [] → bitsand(bits0 + bits, bits2 + bits1) = bitsand(bits0, bits2) + bitsand(bits, bits1)
Proof step 587:
¬(#(false ' + true ' + bits) = # bits1 ∧ bits2 + mklist(false, n - 1) ≠ [] ∧ bits3 ≠ [] ∧ false ' + true ' + bits ≠ []), sgn(mklist(false, n - 1) + false ' + true ' + bits) = false ' + true ' + bits, # bits1 = 2 + # bits ⊦ n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits1, false ' + true ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(false, n - 1)) + false ' + true ' + bits, bits3 + bits1))), bits3 = [], bits3 + bits1 = []
Proof step 595:
#(false ' + true ' + bits) = # bits1 ∧ bits2 + mklist(false, n - 1) ≠ [] ∧ bits3 ≠ [] ∧ false ' + true ' + bits ≠ [], sgn(mklist(false, n - 1) + false ' + true ' + bits) = false ' + true ' + bits, # bits1 = 2 + # bits ⊦ n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits1, false ' + true ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits2 + mklist(false, n - 1), bits3) + bitsand(false ' + true ' + bits, bits1))), bits3 = [], bits3 + bits1 = []

Rule argument

name: bitsand-app rotate: F subst: [bits1, bits2, bits, bits0] → [bits1, bits3, false ' + true ' + bits, bits2 + mklist(false, n - 1)]

Additional information

Used terms: bits1, bits3, false ' + true ' + bits, bits2 + mklist(false, n - 1)