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Proof step 7 from proof succ-truein-01 (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 8:
⊦ (∀ bits1. # bits1 < #(bits0 + true ') → true → true ∈ bits1 +1) → true ∈ (bits0 + true ')+1

Rule argument

indvar: boolvar

Additional information

Used simplifier rules: succ-zero: ⊦ (bits + false ')+1 = bits + true;%bool freely generated by true, false;;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;