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≡stand for the identity type or judgemental equality? What isδ? $\endgroup$Γ (Δ ⊦ α : A) (Δ ⊦ β : a₀ ≡ α) ⊦ B typeis supposed to mean. What is a context, precisely? What are the judgement forms? You're changing these notions in a fundamental way, so you should explain the changes. $\endgroup$≡stands for the identity type, like in Agda. Regardingδ: just like we use the notationx. tto stand for a familytin the background context extended by somex : ?, I haveδ.tstanding for a familytin the background context extended by a telescopeδ : ?. In that particular caseδ : Δ. A context is a snoc-list of families of types (where families can depend on preceding families). Families can be eliminated just like variables in normal MLTT, but now we need to provide an instance of the context the family depends on. $\endgroup$(x : A)with dependence on family(Δ ⊦ x : A)$\endgroup$