Theorems · Definition · general topology
PiNat.dist
{E : ℕ → Type u_1} → Dist ((n : ℕ) → E n)The distance function on a product space Π n, E n, given by dist x y = (1/2)^n where n is
the first index at which x and y differ.
- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Diststatement · cited by 35
- PiNat.firstDiffproof · cited by 23
Cited by12
Results whose statement or proof uses this declaration.
- PiNat.dist_eq_of_nestatement · cited by 7
- PiNat.mem_cylinder_iff_dist_lestatement · cited by 4
- PiNat.apply_eq_of_dist_ltstatement · cited by 3
- PiNat.dist_commstatement · cited by 2
- PiNat.dist_selfstatement · cited by 2
- PiNat.dist_le_onestatement · cited by 1
- PiNat.dist_nonnegstatement · cited by 1
- PiNat.dist_triangle_nonarchstatement · cited by 1
- PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinderstatement · cited by 0
- PiNat.dist_trianglestatement · cited by 0
- PiNat.eq_of_dist_eq_zerostatement · cited by 0
- PiNat.isOpen_iff_diststatement · cited by 0