A note on metatheory

Our metatheory is extensional Martin-Lof type theory with:

• A type of types $\mathsf{Set}$ (ignoring levels for now)
• Dependent function types $(x:A)\to Bx$
• Dependent product types $(x:A)\times Bx$
• Unit type, $\mathsf{tt}:\top$
• Implicit arguments $\{x:A\}\to Bx$, and sometimes even the presence of implicit arguments is implicit, as in $\mathsf{map}:(A\to B)\to FA\to FB$
• Judgmental equality $a\equiv b$
• Definitional equality $fx:\equiv y$
• Equality types $(-=-):\{A:\mathsf{Set}\}\to A\to A\to \mathsf{Set}$