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In 9.6.9.1. Generalising the deriving clause

Notionally, the compiler derives an instance declaration of the form

instance Num Int => Num Dollars

which just adds or removes the newtype constructor according to the type.

which I find weird, I so I decided to check the actual derived instance

$ ghci -ignore-dot-ghci
GHCi, version 8.1.20160503: http://www.haskell.org/ghc/  :? for help
Prelude> :set -ddump-deriv
Prelude> :set -XGeneralizedNewtypeDeriving
Prelude> newtype Dollar = Dollar Int deriving Num

==================== Derived instances ====================
Derived instances:
  instance GHC.Num.Num Ghci1.Dollar where
    [...]

and neither found it there nor in the :info

Prelude> :info Num
class Num a where
  [...]
instance [safe] Num Dollar -- Defined at <interactive>:3:38

and while actually defining instance Num Int => Num Dollar gives you this awkward encounter

$ ghci -ignore-dot-ghci
GHCi, version 8.1.20160503: http://www.haskell.org/ghc/  :? for help
Prelude> data Dollar 
Prelude> instance Num Int => Num Dollar

<interactive>:2:10: error:
    • Non type-variable argument in the constraint: Num Int
      (Use FlexibleContexts to permit this)
    • In the context: Num Int
      While checking an instance declaration
      In the instance declaration for ‘Num Dollar’

Prelude> :set -XFlexibleContexts 
Prelude> instance Num Int => Num Dollar

<interactive>:4:10: error:
    • The constraint ‘Num Int’ is no smaller than the instance head
      (Use UndecidableInstances to permit this)
    • In the instance declaration for ‘Num Dollar’

Prelude> :set -XUndecidableInstances 
Prelude> instance NumPrelude Int => Num Dollar

<interactive>:6:10: warning: [-Wsimplifiable-class-constraints]
    The constraint ‘Num Int’ matches an instance declaration
    instance Num Int -- Defined in ‘GHC.Num’
    This makes type inference very fragile;
      try simplifying it using the instance

<interactive>:6:10: warning: [-Wmissing-methods]
    • No explicit implementation for
        ‘+’, ‘*’, ‘abs’, ‘signum’, ‘fromInteger’, and (either ‘negate’
                                                              or
                                                              ‘-’)
    • In the instance declaration for ‘Num Dollar’

Prelude> :info Dollar
data Dollar     -- Defined at <interactive>:1:1
instance [safe] Num Int => Num Dollar
  -- Defined at <interactive>:6:10

Note that it appears with the context in :info so I wonder in what way that instance declaration is correct