Appendix 3
Prop and Logical Operators in Impredicative MTTs
In impredicative MTTs like UTT (Luo 1994), there is the internal totality Prop of all logical propositions and we can define all of the other logical operators by means of ∀.
A3.1. Prop
A3.2. Logical operators
Here are the definitions of the logical operators by means of ∀ (a special case of Π) in an impredicative type theory (see, for example, section 5.1 of Luo (1994)).
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