Section 5.4: Wrong simplification for checkCompany

Please quote the text that is incorrect:

One more simplification is possible. For every Applicative, pure f <*> E is equivalent to f <$> E. In other words, using seq to apply a function that was placed into the Applicative type using pure is overkill, and the function could have just been applied using Functor.map. This simplification yields:
def checkCompany (input : RawInput) :
Validate (Field × String) LegacyCheckedInput :=
checkThat (input.birthYear == "FIRM")
"birth year" "FIRM if a company" *>
.company <$> checkName input.name

In what way is this incorrect?

This simplification is technically incorrect, because:

The second definition of checkCompany yields to the following expansion:

Seq.seq
  (SeqRight.seqRight (checkThat (BEq.beq myInput.birthYear "FIRM") "birth year" "FIRM is a company") fun x ↦
    pure LegacyCheckedInput.company)
  fun x ↦ checkName myInput.name : Validate (Prod Field String) LegacyCheckedInput

and the third one using map yields to:

SeqRight.seqRight (checkThat (BEq.beq myInput.birthYear "FIRM") "birth year" "FIRM is a company") fun x ↦
  Functor.map LegacyCheckedInput.company (checkName myInput.name) : Validate (Prod Field String) LegacyCheckedInput

Proposed Correction

Add necessary parenthesis to the second checkCompany implementation:

def checkCompany (input : RawInput) : Validate (Field × String) LegacyCheckedInput :=
    checkThat (input.birthYear == "FIRM") "birth year" "FIRM is a company" *>
    (pure .company <*> checkName input.name)

this yields to the following expansion:

SeqRight.seqRight (checkThat (BEq.beq myInput.birthYear "FIRM") "birth year" "FIRM is a company") fun x ↦
  Seq.seq (pure LegacyCheckedInput.company) fun x ↦
    checkName myInput.name : Validate (Prod Field String) LegacyCheckedInput

which is consistent tho the third implementation.

Review Section 5.4 and locate the quoted checkCompany examples in the documentation. Compare the second implementation with the stated Applicative simplification and the expansion shown in the issue; update the example with the necessary parentheses so it is consistent with the third implementation.