Hypercube.lean`

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2 declarations, 0 contain sorry, 0 declared as axioms

The hypercube graph

SimpleGraph.hypercube n is the graph Qₙ on the n-bit vectors, with two vectors adjacent when they differ in exactly one coordinate. It has 2 ^ n vertices and n * 2 ^ (n - 1) edges.

Imports (2)

Imported by 1 file

FormalConjecturesForMathlib.lean

def SimpleGraph.hypercube hypercube n is the n-dimensional hypercube graph Qₙ: the vertices are the n-bit vectors, and two vertices are adjacent when they differ in exactly one coordinate line 37 source
Source documentation
hypercube n is the n-dimensional hypercube graph Qₙ: the vertices are the n-bit vectors, and two vertices are adjacent when they differ in exactly one coordinate.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, SimpleGraph, Fin, Bool
Proof uses: SimpleGraph.mk, Eq, Finset.card, Finset.filter, Ne, Finset.univ, OfNat.ofNat
6 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
def hypercube (n : ℕ) : SimpleGraph (Fin n → Bool) where
…
```
theorem SimpleGraph.hypercube_adj line 43 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Fin, Bool, Iff, SimpleGraph.Adj, SimpleGraph.hypercube, Eq, Finset.card, Finset.filter, Ne, Finset.univ, OfNat.ofNat
Proof uses: Iff.rfl
4 instances, coercions and auxiliary constants left out.