These files are the supporting materials for the paper "Formally Verifying an Algorithm Based on Interval Arithmetic for Checking Transversality" by Marcio Gameiro and Panagiotis Manolios, ACL2-2004. To certify using ACL2 or ACL2(r) v2.9, in the ground-zero theory type: (ld "certify.lsp") If you are on a system that supports "make", then to certify using ACL2 you can simply type "make".