Proving theorems and properties on B models, recursively defined functions is a convenient tool which is missing in B proofs. The main contribution of this paper is the definition of a new theory without new concrete types and without axioms to enable the use of constructions by induction. This theory has been specified and proved within the Theory Plugin in Rodin. This induction theory clearly improves the existing B prover. This is illustrated in this paper by the implementation of ZFC in the Theory Plugin.