import NNG.Metadata
import NNG.MyNat.Addition
import NNG.MyNat.Theorems.Proposition

Game "NNG"
World "Proposition"
Level 9
Title "a big maze."

open MyNat

Introduction
"
Now move onto advanced proposition world, where you will see
how to prove goals such as `P ∧ Q` ($P$ and $Q$), `P ∨ Q` ($P$ or $Q$),
`P ↔ Q` ($P\\iff Q$).
You will need to learn five more tactics: `split`, `cases`,
`left`, `right`, and `exfalso`,
but they are all straightforward, and furthermore they are
essentially the last tactics you
need to learn in order to complete all the levels of the Natural Number Game,
including all the 17 levels of Inequality World. 
"

Statement
"There is a way through the following maze."
    (A B C D E F G H I J K L : Prop)
    (f1 : A → B) (f2 : B → E) (f3 : E → D) (f4 : D → A) (f5 : E → F)
    (f6 : F → C) (f7 : B → C) (f8 : F → G) (f9 : G → J) (f10 : I → J)
    (f11 : J → I) (f12 : I → H) (f13 : E → H) (f14 : H → K) (f15 : I → L) : A → L := by
  -- cc -- TODO: `cc` is not ported yet.
  sorry

Conclusion
"

"