Theorems · Theorem · functional analysis
BoundedContinuousFunction.abs_sub_coe_le_dist
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : SeminormedAddCommGroup β]
(f g : BoundedContinuousFunction α β) {x : α}, ‖f x - g x‖ ≤ dist f g- Cited by
- 1 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.diststatement · cited by 1,539
- BoundedContinuousFunctionstatement and proof · cited by 511
- dist_eq_normproof · cited by 182
- BoundedContinuousFunction.norm_coe_le_normproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.abs_diff_coe_le_distproof · cited by 0