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Proof step 7 from proof succ-true (previous step)

(bits0 + boolvar ')+1 = true ', ∀ bits1. # bits1 < #(bits0 + boolvar ') → true → (bits1 +1 = true ' ↔ bits1 = false ' ∨ bits1 = []) ⊦ bits0 + boolvar ' = false '

User applied rule structural induction

And closed the goal!

Rule argument

indvar: boolvar

Additional information

Used simplifier rules: succ-rec: ⊦ (bits + true ')+1 = bits +1 + false;%succ-empty-01: ⊦ ¬ bits +1 ≠ [] ↔ false;%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 + boolvar0 ' ↔ (boolvar ↔ boolvar0) ∧ bits = [];