Apply suggestions from code review

Co-authored-by: Robert Hensing <[email protected]>

Author: Ericson2314

doc/manual/source/store/build-trace.md

@@ -7,10 +7,10 @@
 > and subject to change.
 
 The *build trace* is a [memoization table](https://en.wikipedia.org/wiki/Memoization) for builds.
-It maps the the inputs of builds to the outputs of builds.
+It maps the inputs of builds to the outputs of builds.
 Concretely, that means it maps [derivations][derivation] to maps of [output] names to [store objects][store object].
 
-In general the derivations used as a key should be be [*resolved*](./resolution.md).
+In general the derivations used as a key should be [*resolved*](./resolution.md).
 A build trace with all-resolved-derivation keys is also called a *base build trace* for extra clarity.
 If all the resolved inputs of a derivation are content-addressed, that means the inputs will be fully determined, leaving no ambiguity for what build was performed.
 (Input-addressed inputs however are still ambiguous. They too should be locked down, but this is left as future work.)

doc/manual/source/store/derivation/outputs/input-address.md

@@ -123,7 +123,7 @@ If the outputs are [content-addressed](./content-address.md), then it computes a
 > In the [fixed](./content-address.md#fixed) content-addressing case, the outputs' content addresses are statically specified in advance, so this always just works.
 > (The fixed case is what the pseudo-code shows.)
 >
-> In the [floating](./content-address.md#floating) case, the content addresses are not specified in advanced.
+> In the [floating](./content-address.md#floating) case, the content addresses are not specified in advance.
 > This is what the "or get from [build trace](@docroot@/store/build-trace.md) if floating" comment refers to.
 > In this case, the algorithm is *stuck* until the input in question is built, and we know what the actual contents of the output in question is.
 >
@@ -133,7 +133,7 @@ If the outputs are [content-addressed](./content-address.md), then it computes a
 
 The recursion in the algorithm is potentially inefficient:
 it could call itself once for each path by which a subderivation can be reached, i.e., `O(V^k)` times for a derivation graph with `V` derivations and with out-degree of at most `k`.
-In the actual implementation, [memoisation]((https://en.wikipedia.org/wiki/Memoization) is used to reduce this cost to be proportional to the total number of `inputDrvOutputs` encountered.
+In the actual implementation, [memoisation](https://en.wikipedia.org/wiki/Memoization) is used to reduce this cost to be proportional to the total number of `inputDrvOutputs` encountered.
 
 ### Semantic properties