| bits1 = bits4 + boolvar1 ', bitsand(true ' + bits3, true ' + bits2) = false ' + bits4, boolvar ∧ boolvar0 ↔ boolvar1, ∀ bits1, bits, bits0. # bits0 < #(bits3 + boolvar ') → bitsand(true ' + bits0, true ' + bits) = false ' + bits1 → false ⊦ bits1 = [], boolvar ∧ boolvar0 ∧ ¬ true ∈ bits1 |
bitsand(true ' + bits3, true ' + bits2) = false ' + bits4, ∀ bits1, bits, bits0. # bits0 < #(bits3 + boolvar ') → bitsand(true ' + bits0, true ' + bits) = false ' + bits1 → false ⊦
Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar ' ≠ [];