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Proof step 44 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: and-notempty-02: ⊦ bits0 ≠ [] → bitsand(boolvar ' + bits, bits0) ≠ [];% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n