Decidable adjacency in a disjoint sum #
[UPSTREAM] candidate for Mathlib/Combinatorics/SimpleGraph/Sum.lean: the adjacency of a
disjoint sum of two graphs with decidable adjacency is decidable.
@[instance_reducible]
instance
SimpleGraph.instDecidableRelSumAdjSum_linglib
{V : Type u_1}
{W : Type u_2}
{G : SimpleGraph V}
{H : SimpleGraph W}
[DecidableRel G.Adj]
[DecidableRel H.Adj]
:
DecidableRel (G ⊕g H).Adj
Equations
- SimpleGraph.instDecidableRelSumAdjSum_linglib (Sum.inl val) (Sum.inl val_1) = decidable_of_iff' (G.Adj val val_1) ⋯
- SimpleGraph.instDecidableRelSumAdjSum_linglib (Sum.inr val) (Sum.inr val_1) = decidable_of_iff' (H.Adj val val_1) ⋯
- SimpleGraph.instDecidableRelSumAdjSum_linglib (Sum.inl val) (Sum.inr val_1) = isFalse ⋯
- SimpleGraph.instDecidableRelSumAdjSum_linglib (Sum.inr val) (Sum.inl val_1) = isFalse ⋯