Is a Farmer villager required to breed?

In a village I found in desert, all villagers died, except the Librarian. I cured a Zombie Villager, that turned out to be another Librarian.

As the wiki describes:

Additionally, villagers must be “willing” in order to breed. After
mating, they will no longer be willing, and must be made willing
again.

Villagers may become willing when the player trades with them.
Willingness is granted the first time a new offer is traded, or at a
one-in-five chance on subsequent trades. Green particles will appear
if the villager becomes willing by trading. This will not cause them
to immediately seek out a mate, however.

Villagers can also become willing by having either 3 bread, 12 carrots
or 12 potatoes in one stack in their inventory. Any villager with an
excess of food (usually farmers) will throw food to other villagers,
allowing them to pick it up and obtain enough food to become willing.
You can also throw bread, carrots, or potatoes at the villagers
yourself to encourage breeding. Villagers will consume the required
food upon becoming willing.

I have traded with them until they don’t want paper anymore, so I traded for the enchanted books, then traded with paper again. I gave them lots of bread, potatoes and carrots. None of them shows hearts, and I ran low on Emeralds, as I had traded them for enchanted books.

I’m planning to cure one more villager. I have searched how to breed and most tutorial uses the example of the Farmer. I can’t find any mechanics that list needing a Farmer.

Is a Farmer villager required to breed?
If it is, do I need both Farmers to breed, or just one of them?
If it’s not, is there any chance for my two Librarians breeding?
Are there new mechanics on the latest 1.8.7 version of Minecraft?