documentation: drop double 'the'

doc/languages-frameworks/android.section.md

@@ -95,7 +95,7 @@ $ nix-build
 
 The Android SDK gets deployed with all desired plugin versions.
 
-We can also deploy subsets of the Android SDK. For example, to only the the
+We can also deploy subsets of the Android SDK. For example, to only the
 `platform-tools` package, you can evaluate the following expression:
 
 ```nix

doc/languages-frameworks/rust.section.md

@@ -203,7 +203,7 @@ argument and returns a set that contains all attribute that should be
 overwritten.
 
 For more complicated cases, such as when parts of the crate's
-derivation depend on the the crate's version, the `attrs` argument of
+derivation depend on the crate's version, the `attrs` argument of
 the override above can be read, as in the following example, which
 patches the derivation:
 

doc/stdenv/cross-compilation.xml

@@ -348,12 +348,12 @@ nix-build '<nixpkgs>' --arg crossSystem '{ config = "<arch>-<os&g
       </para>
      </listitem>
     </orderedlist>
-    In each stage, <varname>pkgsBuildHost</varname> refers the the previous stage, <varname>pkgsBuildBuild</varname> refers to the one before that, and <varname>pkgsHostTarget</varname> refers to the current one, and <varname>pkgsTargetTarget</varname> refers to the next one. When there is no previous or next stage, they instead refer to the current stage. Note how all the invariants regarding the mapping between dependency and depending packages' build host and target platforms are preserved. <varname>pkgsBuildTarget</varname> and <varname>pkgsHostHost</varname> are more complex in that the stage fitting the requirements isn't always a fixed chain of "prevs" and "nexts" away (modulo the "saturating" self-references at the ends). We just special case each instead. All the primary edges are implemented is in <filename>pkgs/stdenv/booter.nix</filename>, and secondarily aliases in <filename>pkgs/top-level/stage.nix</filename>.
+    In each stage, <varname>pkgsBuildHost</varname> refers to the previous stage, <varname>pkgsBuildBuild</varname> refers to the one before that, and <varname>pkgsHostTarget</varname> refers to the current one, and <varname>pkgsTargetTarget</varname> refers to the next one. When there is no previous or next stage, they instead refer to the current stage. Note how all the invariants regarding the mapping between dependency and depending packages' build host and target platforms are preserved. <varname>pkgsBuildTarget</varname> and <varname>pkgsHostHost</varname> are more complex in that the stage fitting the requirements isn't always a fixed chain of "prevs" and "nexts" away (modulo the "saturating" self-references at the ends). We just special case each instead. All the primary edges are implemented is in <filename>pkgs/stdenv/booter.nix</filename>, and secondarily aliases in <filename>pkgs/top-level/stage.nix</filename>.
    </para>
 
    <note>
     <para>
-     Note the native stages are bootstrapped in legacy ways that predate the current cross implementation. This is why the the bootstrapping stages leading up to the final stages are ignored inthe previous paragraph.
+     Note the native stages are bootstrapped in legacy ways that predate the current cross implementation. This is why the bootstrapping stages leading up to the final stages are ignored inthe previous paragraph.
     </para>
    </note>