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Proof step 12 from proof add-ones-grlen (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
∀ bits0, bits, n. # bits0 < # [] → # bits = n + 1 + # bits0 ∧ # bits0 < # bits → bits = [] ∨ bitsand(bits, true ' + bits0) = (true ' + mklist(true, n)) + bits0 ∨ false ∈ bits ⊦ bits2 = [], bitsand(true ' + bits2, true ') = true ' + bits2, false ∈ bits2

Rule argument

Additional information

Used simplifier rules: and-onel-02: ⊦ bitsand(true ', boolvar ' + bits) = boolvar ' + bits;% ⊦ ¬ false ∈ bits → mklist(true, # bits) = bits;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ bits = bits0 + bits ↔ bits0 = [];% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ ¬ boolvar ∈ [];% ⊦ m ≤ 0 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0;% ⊦ 0 ≤ m;% ⊦ bits + [] = bits;% ⊦ 0 + m = m;% ⊦ # [] = 0;% ⊦ boolvar ' = boolvar0 ' + bits ↔ (boolvar ↔ boolvar0) ∧ bits = [];%⊦ ¬ boolvar ∈ boolvar0 ' + bits ↔ ¬(boolvar ↔ boolvar0) ∧ ¬ boolvar ∈ bits;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ boolvar ' + bits ≠ [];% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ boolvar + bits = boolvar ' + bits;