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Proof step 5 from proof succ-prefix (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 6:
⊦ (∀ bits2, bits. # bits2 < #(bits1 + true ') → true → (bits + false ' + bits2)+1 = bits + (false ' + bits2)+1) → (bits + false ' + bits1 + true ')+1 = bits + (false ' + bits1 + 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 + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;