Modular approaches to verifying interprocedural programs involve learning summaries for individual procedures rather than verifying a monolithic program. Modern approaches based on use of Satisfiability Modulo Theory (SMT) solvers have made much progress in this direction. However, it is still challenging to handle mutual recursion and to derive adequate procedure summaries using scalable methods. We propose a novel modular verification algorithm that addresses these challenges by learning lemmas about the relationships among procedure summaries and by using bounded environments in SMT queries. We have implemented our algorithm in a tool called Clover and report on a detailed evaluation that shows that it outperforms existing automated tools on benchmark programs with mutual recursion while being competitive on standard benchmarks.