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Proof step 7 from proof and-notone-01 (previous step)

bits = boolvar + bits3, bitsand(bits, false ' + bits0) = true ' + bits1, bits = boolvar ', ∀ bits2, bits0, bits1. # bits2 < # bits → bitsand(bits2, false ' + bits0) = true ' + bits1 → bits2 = [] ⊦ bits = [], bits0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
bitsand(boolvar ', false ' + bits0) = true ' + bits1, ∀ bits2, bits0, bits1. # bits2 < #(boolvar + []) → bitsand(bits2, false ' + bits0) = true ' + bits1 → bits2 = [] ⊦ bits0 = []

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ bits + [] = bits;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' = boolvar0 ' + bits ↔ (boolvar ↔ boolvar0) ∧ bits = [];% ⊦ boolvar + bits = boolvar ' + bits;