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Proof step 67 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: and-notempty-02: ⊦ bits0 ≠ [] → bitsand(boolvar ' + bits, bits0) ≠ [];% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ∈ sgn(boolvar0 ' + bits) ↔ boolvar ∈ boolvar0 ' + bits;% ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits; (forward)% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ bits + [] = bits;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 + m = m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ [] + bits = bits;% ⊦ mklist(boolvar, 0) = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;