In the novel, The lion, the Witch and Wardrobe. Can you please help me find examples/proof of genres discussed in the book.

I am not sure I totally understand your question, but I
will attempt to answer it. If this is not what you are looking for, please repost your
question and be more specific.

When Lucy tries to explain
to her 3 other siblings about what she discovered in the wardrobe, the older three
accuse her of getting too carried away with her fantasies, so this is a reference to the
fact that Lucy may have been reading too many fairy tale
books.

Mr. Beaver tells the children the ancient prophecy
about the White Witch and Aslan. This can also be interpreted as fantasy to the
children, who come from another world where the rules are different. In their world,
animals cannot talk and do not have “prophecies” – this prophecy is not fantasy to Mr.
Beaver, however, but it is to the children while they are in
Narnia.

There is a reference to fantasy and children’s
literature in Chapter 10 when the children encounter Santa Claus. He tells the children
the Witch’s power is weakening and gives them tools for presents. They later use these
tools to get them out of jams. Peter receives a sword and a shield, Susan receives a bow
and arrow and Lucy receives a dagger and a bottle of magic elixir that can cure
anything.

Another fantasy genre that is referred to in this
novel is the tales associated with Knights of the Round Table. The children are supposed
to rule in Narnia, and eventually they do become its rulers, but first they are knighted
as a preparation to enter battle with the White Witch. They become Aslan’s knights, even
the girls.

In chapter 15, Lucy and Susan come upon Aslan's
dead body on the stone altar, but there are mice nibbling at the ropes that bind him.
This is a reference to one of Aesop's tales, "The Lion and the Mouse" where the tiny
mouse helps the lion get rid of a splinter in his paw.