You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
43 lines
1.2 KiB
Plaintext
43 lines
1.2 KiB
Plaintext
import NNG.Metadata
|
|
import NNG.MyNat.Addition
|
|
|
|
Game "NNG"
|
|
World "Function"
|
|
Level 9
|
|
Title ""
|
|
|
|
open MyNat
|
|
|
|
Introduction
|
|
"
|
|
I asked around on Zulip and apparently there is not a tactic for this, perhaps because
|
|
this level is rather artificial. In world 6 we will see a variant of this example
|
|
which can be solved by a tactic. It would be an interesting project to make a tactic
|
|
which could solve this sort of level in Lean.
|
|
|
|
You can of course work both forwards and backwards, or you could crack and draw a picture.
|
|
"
|
|
|
|
Statement
|
|
"Given a bunch of functions, we can define another one."
|
|
(A B C D E F G H I J K L : Type)
|
|
(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
|
|
intro a
|
|
apply f15
|
|
apply f11
|
|
apply f9
|
|
apply f8
|
|
apply f5
|
|
apply f2
|
|
apply f1
|
|
exact a
|
|
|
|
|
|
Conclusion
|
|
"
|
|
That's the end of Function World! Next it's Proposition world, and the tactics you've learnt in Function World are enough
|
|
to solve all nine levels! In fact, the levels in Proposition world might look strangely familiar$\\ldots$.
|
|
"
|