720.lean`

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

5 declarations, 4 contain sorry, 0 declared as axioms

Erdős Problem 720

References:

erdosproblems.com/720
[Er76c] Erdős, P., Some recent problems and results in graph theory, combinatorics and number theory. Proceedings of the Seventh Southeastern Conference on Combinatorics, Graph Theory, and Computing (Louisiana State Univ., Baton Rouge, La., 1976) (1976), 3-14.
[EFRS78b] Erdős, P. and Faudree, R. J. and Rousseau, C. C. and Schelp, R. H., The size Ramsey number. Period. Math. Hungar. (1978), 145-161.
[Er78] Erdős, Paul, Problems and results in combinatorial analysis and combinatorial number theory. Proceedings of the Ninth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1978) (1978), 29-40.
[Er81] Erdős, P., On the combinatorial problems which I would most like to see solved. Combinatorica (1981), 25-42.
[Er82e] Erdős, Paul, Some of my favourite problems which recently have been solved. (1982), 59--79.
[Be83b] Beck, József, On size Ramsey number of paths, trees, and circuits. I. J. Graph Theory (1983), 115-129.

Imports (1)

FormalConjecturesUtil

abbrev Erdos720.sizeRamseyNumber The size Ramsey number $\hat{R}(G)$ of G: the least number of edges of a graph which is Ramsey for G line 49 source
Source documentation
The size Ramsey number $\hat{R}(G)$ of G: the least number of edges of a graph which is Ramsey for G.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, SimpleGraph, Nat
Proof uses: SimpleGraph.sizeRamsey
```
noncomputable abbrev sizeRamseyNumber {V : Type*} [Fintype V] (G : SimpleGraph V) : ℕ :=
…
```
theorem Erdos720.erdos_720.parts.i sorry line 63 source
depends on sorry what this means
Statement uses: Iff, False, Filter.Tendsto, Nat, Real, HDiv.hDiv, Erdos720.sizeRamseyNumber, Fin, HAdd.hAdd, OfNat.ofNat, SimpleGraph.pathGraph, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
22 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem Erdos720.erdos_720.parts.ii sorry line 74 source
depends on sorry what this means
Statement uses: Iff, True, Filter.Tendsto, Nat, Real, HDiv.hDiv, Erdos720.sizeRamseyNumber, Fin, HAdd.hAdd, OfNat.ofNat, SimpleGraph.pathGraph, HPow.hPow, Filter.atTop, nhds
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
38 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem Erdos720.erdos_720.parts.iii sorry line 86 source
depends on sorry what this means
Statement uses: Iff, True, Filter.Tendsto, Nat, Real, HDiv.hDiv, Erdos720.sizeRamseyNumber, Fin, SimpleGraph.cycleGraph, HPow.hPow, OfNat.ofNat, Filter.atTop, nhds
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
34 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem Erdos720.erdos_720.variants.beck sorry line 94 source
depends on sorry what this means
Statement uses: Exists, Nat, Filter.Eventually, And, LE.le, Erdos720.sizeRamseyNumber, Fin, HAdd.hAdd, OfNat.ofNat, SimpleGraph.pathGraph, HMul.hMul, SimpleGraph.cycleGraph, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
16 instances, coercions and auxiliary constants left out.

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