Editing Calculus of constructions (section)

=== β-equivalence ===

As with the untyped lambda calculus, the calculus of constructions uses a basic notion of equivalence of terms, known as <math>\beta</math>-equivalence. This captures the meaning of <math>\lambda</math>-abstraction:

* <math>(\lambda x:A . B) N =_\beta B(x := N)</math>

<math>\beta</math>-equivalence is a congruence relation for the calculus of constructions, in the sense that

* If <math>A =_\beta B</math> and <math>M =_\beta N</math>, then <math>A M =_\beta B N</math>.