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Proof step 8 from proof succ-truein-01 (previous step)

⊦ (∀ bits1. # bits1 < #(bits0 + true ') → true → true ∈ bits1 +1) → true ∈ (bits0 + true ')+1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ bits. ¬ # bits0 < # bits → true ∈ bits +1 ⊦ true ∈ bits0 +1

Rule argument

Additional information

Used simplifier rules: succ-rec: ⊦ (bits + true ')+1 = bits +1 + false;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar = bits + boolvar ';