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Proof step 373 from proof bitsand-cast (previous step)

sgn(mklist(boolvar, n) + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits2 + mklist(boolvar, n) + boolvar0 ' + bits, bits0))), n = 0, boolvar ↔ boolvar0, bits0 = [], ¬ false ∈ mklist(boolvar, n) ∧ boolvar0 ∧ ¬ false ∈ bits, ¬ true ∈ mklist(boolvar, n) ∧ ¬ boolvar0 ∧ ¬ true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 374:
⊦ n ≠ 0 → mklist(boolvar, n) = mklist(boolvar, n -1) + boolvar '
Proof step 375:
n ≠ 0, sgn((mklist(boolvar, n -1) + boolvar ') + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits2 + (mklist(boolvar, n -1) + boolvar ') + boolvar0 ' + bits, bits0))), n = 0, boolvar ↔ boolvar0, bits0 = [], ¬ false ∈ mklist(boolvar, n -1) + boolvar ' ∧ boolvar0 ∧ ¬ false ∈ bits, ¬ true ∈ mklist(boolvar, n -1) + boolvar ' ∧ ¬ boolvar0 ∧ ¬ true ∈ bits

Rule argument

seq: ⊦ n ≠ 0 → mklist(boolvar, n) = mklist(boolvar, n -1) + boolvar ' subst: [n, boolvar] → [n, boolvar] rotate: F spec: list-last inst: bitlista name: mk-last-02

Additional information

Used terms: n, boolvar