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Proof step 15 from proof and-size-one-01 (previous step)

# bits3 = # bits2, ∀ bits, bits1, bits0. # bits < #(bits3 + boolvar ') → # bits = # bits1 → bits1 = [] ∨ bits0 = [] ∨ bitsand(true ' + bits, bits0 + bits1) = bits0 + bitsand(bits, bits1) ⊦ bits0 = [], bitsand(true ' + bits3, bits0 + bits2) + (boolvar ∧ boolvar0)' = bits0 + bitsand(bits3 + boolvar ', bits2 + boolvar0 '), bits3 ≠ [] ∧ bits2 ≠ []

User applied rule cut formula

And closed the goal!

Rule argument

fma: bits3 = []

Additional information

Used simplifier rules: and-onel-01: ⊦ bits ≠ [] → bitsand(true ', bits) = bits;%and-one: ⊦ bitsand(boolvar ', boolvar0 ') = (boolvar ∧ boolvar0)';% ⊦ # [] = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ [] + bits = bits;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1; Used formulas: bits3 = []