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.
lean4game/server/nng/NNG/Levels/Proposition/Level_7.lean

28 lines
646 B
Plaintext

import NNG.Metadata
import NNG.MyNat.Addition
Game "NNG"
World "Proposition"
Level 7
Title "(P → Q) → ((Q → R) → (P → R))"
open MyNat
Introduction ""
Statement
"From $P\\implies Q$ and $Q\\implies R$ we can deduce $P\\implies R$."
(P Q R : Prop) : (P → Q) → ((Q → R) → (P → R)) := by
Hint (hidden := true)"If you start with `intro hpq` and then `intro hqr`
the dust will clear a bit."
intro hpq
Hint (hidden := true) "Now try `intro hqr`."
intro hqr
Hint "So this level is really about showing transitivity of $\\implies$,
if you like that sort of language."
intro p
apply hqr
apply hpq
exact p