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

⊦ (∀ bits2, bits. # bits2 < #(bits1 + true ') → true → (bits + false ' + bits2)+1 = bits + (false ' + bits2)+1) → (bits + false ' + bits1 + true ')+1 = bits + (false ' + bits1 + true ')+1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ bits0, bits2. ¬ # bits1 < # bits0 → (bits2 + false ' + bits0)+1 = bits2 + (false ' + bits0)+1 ⊦ (bits + false ' + bits1)+1 = bits + (false ' + bits1)+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;% ⊦ bits + bits0 = bits1 + bits0 ↔ bits = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar = bits + boolvar ';