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Proof step 661 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 662:
⊦ ¬ true ∈ bits ∧ (# bits ≤ # bits0 ∨ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits
Proof step 663:
¬(¬ true ∈ mklist(false, m) ∧ (# mklist(false, m) ≤ # bits3 ∨ bits3.first) ∧ mklist(false, m) ≠ [] ∧ bits3 ≠ []), sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bits3 ≤ m ⊦ bits3 + bits1 = [], bits2 + mklist(false, m) = [], bits1 = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(mklist(false, m), bits3) + bitsand(false ' + true ' + bits, bits1))), bits3 = [], bits3.first
Proof step 711:
¬ true ∈ mklist(false, m) ∧ (# mklist(false, m) ≤ # bits3 ∨ bits3.first) ∧ mklist(false, m) ≠ [] ∧ bits3 ≠ [], sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bits3 ≤ m ⊦ bits3 + bits1 = [], bits2 + mklist(false, m) = [], bits1 = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, mklist(false, m) + bitsand(false ' + true ' + bits, bits1))), bits3 = [], bits3.first

Rule argument

name: bitsand-zeros rotate: F subst: [bits0, bits] → [bits3, mklist(false, m)]

Additional information

Used terms: bits3, mklist(false, m)