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We rely on the internal language of presheaf categories. In order to combine the internal languages of multiple presheaf categories, we use Dependent Right Adjoints and Multimodal Type Theory. ... As example applications of these induction principles, we give short and boilerplate-free proofs of canonicity and normalization for some small type theories, and sketch proofs of other metatheoretic results ... In Matthias Blume, Naoki Kobayashi, and Germán Vidal, editors, Functional and Logic Programming, 10th International Symposium, FLOPS 2010, Sendai, Japan, April 19-21, 2010. ...arXiv:2102.11649v2 fatcat:abnprqczb5czpgzmvdbys2uca4