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Proof step 16 from proof and-notone-01 (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 17:
bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast) = (true ' + bits1).butlast, bits0.last ∧ bits3.last ↔ (true ' + bits1).last, ∀ bits2, bits0, bits1. # bits2 < #(boolvar + bits3) → bitsand(bits2, false ' + bits0) = true ' + bits1 → bits2 = [] ⊦ bits1 = [], bits3 = [], bits0 = [], (¬ bits3.last ∨ ¬ bits0.last) ∧ ¬ true ∈ bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast), ¬ (bits3.last ∧ bits0.last) ∈ bits1 ∧ (¬ bits3.last ∨ ¬ bits0.last), (¬ bits0.last ∨ ¬ bits3.last) ∧ ¬ (bits0.last ∧ bits3.last) ∈ bits1, ¬ true ∈ bitsand(boolvar ' + bits3.butlast, false ' + bits0.butlast) ∧ (¬ bits0.last ∨ ¬ bits3.last)

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 = []