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fix build
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robertylewis committed Feb 10, 2020
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3 changes: 1 addition & 2 deletions src/topology/metric_space/gromov_hausdorff.lean
Original file line number Diff line number Diff line change
Expand Up @@ -226,14 +226,13 @@ begin
simp [Aα, Bβ]
end

local attribute [instance, priority 10] inhabited_of_nonempty'

/-- The optimal coupling constructed above realizes exactly the Gromov-Hausdorff distance,
essentially by design. -/
lemma Hausdorff_dist_optimal {α : Type u} [metric_space α] [compact_space α] [nonempty α]
{β : Type v} [metric_space β] [compact_space β] [nonempty β] :
Hausdorff_dist (range (optimal_GH_injl α β)) (range (optimal_GH_injr α β)) = GH_dist α β :=
begin
inhabit α, inhabit β,
/- we only need to check the inequality `≤`, as the other one follows from the previous lemma.
As the Gromov-Hausdorff distance is an infimum, we need to check that the Hausdorff distance
in the optimal coupling is smaller than the Hausdorff distance of any coupling.
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