Update README.md

README.md

@@ -1,16 +1,21 @@
 # Actuary
 
-This is an experimental package where the basic part of actuarial mathematics is formalized using Coq -- proof assistant.
+This is an experimental package where the basic part of actuarial mathematics is formalized using the Coq Proof Assistant.
 
 ## Description of files
 - Basics: Some basic facts of mathematics are collected for the main part of the package.
-- Interest: The theory of interest is formalized, including the present and future value of annuities.
+- Interest: The theory of interest is formalized, including the present and future values of annuities.
 - LifeTable: The life table is defined axiomatically, and is examined mainly from probability theory.
-- Premium: Basic actuarial notations are introduced, including various facts on the present value of annuities, insurance and so on.
+- Premium: Basic actuarial notations are introduced, including various facts on the present values of annuities, insurance and so on.
 - Reserve: The level premium reserve is defined, and some useful formulas are also proved formally.
 - Examples: Some applications of this package are shown.
 
 ## Notice
-- This package uses mathcomp and Coquelicot.
+- This package uses MathComp and Coquelicot.
 - Classical logic is assumed.
-- This package will be frequently updated, and may not be backward compatible.
+- The following functions are set to be coercions:
+  - INR : nat >-> R
+  - IZR : Z >-> R
+- The infix notation "^" is redefined as Rpower, and the original function pow is represented as ".^".
+- This package may be frequently updated, and may not be backward compatible.
+- Any advice or comment is welcome.