842.lean`

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L4DEL: Lean4 Domain Explanation Language

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 842

References:

erdosproblems.com/842
[Er92b] Erdős, Paul, Some of my favourite problems in various branches of combinatorics. Matematiche (Catania) (1992), 231-240.
[FlSt92] Fleischner, Herbert and Stiebitz, Michael, A solution to a colouring problem of P. Erdős. Discrete Math. (1992), 39--48.

Imports (1)

FormalConjecturesUtil

def Erdos842.IsTrianglesPlusHamiltonianCycle Documented declaration: IsTrianglesPlusHamiltonianCycle line 39 source
Source documentation
G is a graph on 3n vertices formed by taking n vertex-disjoint triangles T and adding a Hamiltonian cycle C (with all new edges): G = T ⊔ C with T and C edge-disjoint.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: SimpleGraph, Nat
Proof uses: Exists, And, Eq, Max.max, Disjoint, Equiv, Prod, Fin, OfNat.ofNat, Iff, SimpleGraph.Adj, Ne, Prod.fst, HMul.hMul, SimpleGraph.map, Function.Embedding, Equiv.toEmbedding, SimpleGraph.cycleGraph
14 instances, coercions and auxiliary constants left out.
```
def IsTrianglesPlusHamiltonianCycle {V : Type*} (G : SimpleGraph V) (n : ℕ) : Prop :=
…
```
theorem Erdos842.erdos_842 sorry line 53 source
depends on sorry what this means
Statement uses: Iff, True, SimpleGraph, Nat, Erdos842.IsTrianglesPlusHamiltonianCycle, LE.le, ENat, SimpleGraph.chromaticNumber, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.