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Proof step 6 from proof succ-falsein (previous step)

bits ≠ [] → (∃ bits0, boolvar. bits = bits0 + boolvar '), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ false ∈ (false ' + bits0)+1 ⊦ bits = [], false ∈ (false ' + bits)+1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ bits1. # bits1 < #(bits0 + boolvar ') → true → bits1 = [] ∨ false ∈ (false ' + bits1)+1 ⊦ false ∈ (false ' + bits0 + boolvar ')+1

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ bits + boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar ' = bits0 → boolvar ∈ bits0; (forward)