In this paper, we provide an in-depth account of traditional IBL instruction. Understanding the nature and effects of this form of instruction is of growing importance due to the strength and breadth of the IBL movement and its connections to other forms of inquiry in undergraduate mathematics. In this case study of one real analysis course taught by a very experienced instructor and leader in the IBL community, we identify the primary goals this professor set forth for his students and the instructional strategies he employed to help them attain these goals. We observe that many of these practices seek to manage the double bind of proving in the classroom (Herbst "Journal for Research in Mathematics Education," 33(3), 176-203, 2002). Accordingly, we relate and categorize student storylines in the course according to their goal orientation and their level of buy-in to the IBL learning environment. We operationalize orientation and buy-in according to the double bind of the didactic contract by observing whether students focused more on the professor's obligation to provide resources for students to successfully complete the work of the course (and earn good grades) or on his obligation to provide an authentic experience in mathematical proving. Students' with different goal orientation and buy-in profiles took advantage of different aspects the professor's instructional strategies to engage in the course in ways that were productive for them.