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Proof step 19 from proof and-false (previous step)

bitsand(true ' + bits3, true ' + bits2) = (false ' + bits1).butlast, boolvar ∧ boolvar0 ↔ (false ' + bits1).last, ∀ bits1, bits, bits0. # bits0 < #(bits3 + boolvar ') → bitsand(true ' + bits0, true ' + bits) = false ' + bits1 → false ⊦ boolvar ∧ boolvar0 ∧ ¬ true ∈ bits1, ¬ false ∈ bitsand(true ' + bits3, true ' + bits2) ∧ boolvar ∧ boolvar0

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 20:
bitsand(true ' + bits3, true ' + bits2) = (false ' + bits1).butlast, boolvar ∧ boolvar0 ↔ (false ' + bits1).last, ∀ bits1, bits, bits0. # bits0 < #(bits3 + boolvar ') → bitsand(true ' + bits0, true ' + bits) = false ' + bits1 → false ⊦ bits1 = [], boolvar ∧ boolvar0 ∧ ¬ true ∈ bits1, ¬ false ∈ bitsand(true ' + bits3, true ' + bits2) ∧ boolvar ∧ boolvar0

Rule argument

fma: bits1 = []

Additional information

Used simplifier rules: and-notempty-05: ⊦ bitsand(boolvar0 ' + bits, boolvar ' + bits0) ≠ [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar '.butlast = []; Used formulas: bits1 = []