`Compfiles/Imo1964P4.lean`

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International Mathematical Olympiad 1964, Problem 4

Seventeen people correspond by mail with one another -- each one with all the rest. In their letters only three different topics are discussed. Each pair of correspondents deals with only one of the topics. Prove that there are at least three people who write to each other about the same topic.

Imports (4)

Imported by 1 file

Compfiles.lean

theorem Imo1964P4.lemma1 Smaller version of the problem, with 6 (or more) people and 2 topics line 40 source
Source documentation
Smaller version of the problem, with 6 (or more) people and 2 topics.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, DecidableEq, LT.lt, Nat, OfNat.ofNat, Fintype.card, Eq, Exists, Finset, And, Finset.card, Membership.mem, Ne
Proof uses: Nonempty.some, Iff.mp, Nonempty, Fintype.card_pos_iff, Subtype, Eq.mpr, HSub.hSub, id, congrArg, Not, Fintype.card_subtype_compl, lt_tsub_of_add_lt_left, HAdd.hAdd, HMul.hMul, Finset.filter, Finset.univ, Fintype.exists_lt_card_fiber_of_mul_lt_card, of_eq_true, Eq.trans, True and 31 more
49 instances, coercions and auxiliary constants left out.

Tactic trace: 51 steps
Open to load the checked before-and-after goal states.
```
theorem lemma1
    (Person Topic : Type)
    [Fintype Person] [DecidableEq Person]
    [Fintype Topic] [DecidableEq Topic]
    (card_person : 5 < Fintype.card Person)
    (card_topic : Fintype.card Topic = 2)
    (discusses : Person → Person → Topic)
    (discussion_sym : ∀ p1 p2 : Person, discusses p1 p2 = discusses p2 p1) :
    ∃ t : Topic, ∃ s : Finset Person,
      2 < s.card ∧
        ∀ p1 ∈ s, ∀ p2 ∈ s, p1 ≠ p2 → discusses p1 p2 = t := by
…
```
problem Imo1964P4.imo1964_p4 line 111 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, DecidableEq, Eq, Nat, Fintype.card, OfNat.ofNat, Exists, Finset, And, LT.lt, Finset.card, Membership.mem, Ne
Proof uses: Nonempty.some, Iff.mp, Nonempty, Fintype.card_pos_iff, Subtype, of_eq_true, Eq.trans, True, congrFun', congrArg, Not, HSub.hSub, Fintype.card_subtype_compl, congr, Fintype.card_unique, eq_self, HMul.hMul, Eq.mpr, id, Mathlib.Meta.NormNum.isNat_lt_true and 63 more
54 instances, coercions and auxiliary constants left out.

Tactic trace: 90 steps
Open to load the checked before-and-after goal states.