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Proof step 17 from proof add-ones-lelen (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# bits0 ≤ # bits2, ∀ bits1, bits. # bits1 < #(boolvar + (bits2 + boolvar0 ')) → true → ¬ false ∈ bits ∧ # bits ≤ # bits1 ∧ bits ≠ [] → bitsand(bits, bits1) = bits1 ⊦ bitsand(true ' + bits0, boolvar ' + bits2) = boolvar ' + bits2, false ∈ bits0

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ bits + bits0 = bits1 + bits0 ↔ bits = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar ' ≠ [];