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Proof step 10 from proof bitsand-zeros-01 (previous step)

bits1 = bits2 + boolvar ', 1 + # bits1 < # bits, ∀ bits1, bits0. # bits0 < # bits → 1 + # bits1 < # bits0 → bits0 = [] ∨ bitsand(bits0, false ' + bits1) = false ' + mklist(false, # bits1) ∨ true ∈ bits0 ⊦ # bits = 1, bits1 = [], bits = [], bitsand(bits.butlast, false ' + bits2) + (bits.last ∧ boolvar)' = false ' + mklist(false, # bits1), true ∈ bits

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
2 + # bits2 < # bits, ∀ bits1, bits0. # bits0 < # bits → 1 + # bits1 < # bits0 → bits0 = [] ∨ bitsand(bits0, false ' + bits1) = false ' + mklist(false, # bits1) ∨ true ∈ bits0 ⊦ # bits = 1, bits = [], bitsand(bits.butlast, false ' + bits2) + (bits.last ∧ boolvar)' = false ' + false ' + mklist(false, # bits2), true ∈ bits

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ bits + [] = bits;% ⊦ mklist(boolvar, 0) = [];%n ≠ 0 ⊦ mklist(false, (* n)) = false ' + mklist(false, n -1);% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar ' ≠ [];