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Proof step 78 from proof bitsand-cast (previous step)

n0 = m + 1, sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits1), n0 + 1 + # bits1 < m + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), # bits0 ≤ 2 + # bits1, bits0.first, n0 + 1 + # bits1 < n, n ≤ m + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n ⊦ n0 = 0, boolvar ↔ boolvar0, bits0 = [], m = 0, mklist(boolvar, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = lastn(n, mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), 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) ≠ [];% ⊦ m < n → n ≠ 0;% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ m + n < m0 → m + n < m0 + n0;% ⊦ m < m + n ↔ n ≠ 0;% ⊦ m +1 = m + 1;% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits;% ⊦ # bits = 0 ↔ bits = [];% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ 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)% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≠ 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;