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Proof step 57 from proof bitsand-cast (previous step)

(mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)).first ↔ boolvar, sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, # bits0 ≤ 2 + # bits1, bits0.first, n0 + 1 + # bits1 < n, (n0 - 1) + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, n0 + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) ≤ n + 1 ⊦ mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = [], n0 = 0, boolvar ↔ boolvar0, bits0 = [], mklist(boolvar, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) = mklist(boolvar, n - (n0 - 1) + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) + mklist(boolvar, n0 - 1), boolvar ∧ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n) subst: [n, m, boolvar] → [n0 - 1, n - (n0 - 1) + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), boolvar] rotate: T spec: list-last inst: bitlista name: mk-plus

Additional information

Used terms: n0 - 1, n - (n0 - 1) + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), boolvar