diff --git a/README.md b/README.md
index 25fde42..abb3c5c 100644
--- a/README.md
+++ b/README.md
@@ -13,12 +13,12 @@ Follow the instructions on https://github.com/coq-community/templates to regener
 
 
 This library provides `ring` and `field` tactics for Mathematical Components,
-that work with any `comRingType`s and `fieldType`s, respectively. Their
-instance resolution is done through canonical structure inference. Therefore,
-they work with abstract rings and do not require `Add Ring` and `Add Field`
-commands. Another key feature of this library is that they automatically push
-down ring morphisms to leaves of ring and field expressions before
-normalization to the Horner form.
+that work with any `comRingType` and `fieldType` instances, respectively.
+Their instance resolution is done through canonical structure inference.
+Therefore, they work with abstract rings and do not require `Add Ring` and
+`Add Field` commands. Another key feature of this library is that they
+automatically push down ring morphisms and additive functions to leaves of
+ring/field expressions before normalization to the Horner form.
 
 ## Meta
 
@@ -54,7 +54,7 @@ make install
 
 
 ## Credits
-The way we adapt internals of Coq's `ring` and `field` tactics to algebraic
-structures of the Mathematical Components library is inspired by the
+The way we adapt the internals of Coq's `ring` and `field` tactics to
+algebraic structures of the Mathematical Components library is inspired by the
 [elliptic-curves-ssr](https://github.com/strub/elliptic-curves-ssr) library by
 Evmorfia-Iro Bartzia and Pierre-Yves Strub.
diff --git a/coq-mathcomp-algebra-tactics.opam b/coq-mathcomp-algebra-tactics.opam
index b88830c..0dc3e50 100644
--- a/coq-mathcomp-algebra-tactics.opam
+++ b/coq-mathcomp-algebra-tactics.opam
@@ -10,15 +10,15 @@ dev-repo: "git+https://github.com/math-comp/algebra-tactics.git"
 bug-reports: "https://github.com/math-comp/algebra-tactics/issues"
 license: "CECILL-B"
 
-synopsis: "Reflexive ring and field tactics for Mathematical Components"
+synopsis: "Ring and field tactics for Mathematical Components"
 description: """
 This library provides `ring` and `field` tactics for Mathematical Components,
-that work with any `comRingType`s and `fieldType`s, respectively. Their
-instance resolution is done through canonical structure inference. Therefore,
-they work with abstract rings and do not require `Add Ring` and `Add Field`
-commands. Another key feature of this library is that they automatically push
-down ring morphisms to leaves of ring and field expressions before
-normalization to the Horner form."""
+that work with any `comRingType` and `fieldType` instances, respectively.
+Their instance resolution is done through canonical structure inference.
+Therefore, they work with abstract rings and do not require `Add Ring` and
+`Add Field` commands. Another key feature of this library is that they
+automatically push down ring morphisms and additive functions to leaves of
+ring/field expressions before normalization to the Horner form."""
 
 build: [make "-j%{jobs}%" ]
 install: [make "install"]
diff --git a/meta.yml b/meta.yml
index 6dd6d49..5be3f9d 100644
--- a/meta.yml
+++ b/meta.yml
@@ -6,16 +6,16 @@ organization: math-comp
 action: true
 
 synopsis: >-
-  Reflexive ring and field tactics for Mathematical Components
+  Ring and field tactics for Mathematical Components
 
 description: |-
   This library provides `ring` and `field` tactics for Mathematical Components,
-  that work with any `comRingType`s and `fieldType`s, respectively. Their
-  instance resolution is done through canonical structure inference. Therefore,
-  they work with abstract rings and do not require `Add Ring` and `Add Field`
-  commands. Another key feature of this library is that they automatically push
-  down ring morphisms to leaves of ring and field expressions before
-  normalization to the Horner form.
+  that work with any `comRingType` and `fieldType` instances, respectively.
+  Their instance resolution is done through canonical structure inference.
+  Therefore, they work with abstract rings and do not require `Add Ring` and
+  `Add Field` commands. Another key feature of this library is that they
+  automatically push down ring morphisms and additive functions to leaves of
+  ring/field expressions before normalization to the Horner form.
 
 authors:
 - name: Kazuhiko Sakaguchi
@@ -65,8 +65,8 @@ namespace: mathcomp.algebra_tactics
 
 documentation: |-
   ## Credits
-  The way we adapt internals of Coq's `ring` and `field` tactics to algebraic
-  structures of the Mathematical Components library is inspired by the
+  The way we adapt the internals of Coq's `ring` and `field` tactics to
+  algebraic structures of the Mathematical Components library is inspired by the
   [elliptic-curves-ssr](https://github.com/strub/elliptic-curves-ssr) library by
   Evmorfia-Iro Bartzia and Pierre-Yves Strub.