Theorems · Theorem · Lie groups
ContinuousOn.sub
∀ {G : Type u_1} {X : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace G] [inst_2 : Sub G]
[ContinuousSub G] {f g : X → G} {s : Set X}, ContinuousOn f s → ContinuousOn g s → ContinuousOn (f - g) s- Defined in
- Mathlib.Topology.Algebra.Group.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousOnstatement and proof · cited by 1,411
- ContinuousSubstatement and proof · cited by 48
- ContinuousWithinAt.subproof · cited by 10
Cited by21
Results whose statement or proof uses this declaration.
- ContinuousOn.fun_subproof · cited by 18
- DiffContOnCl.subproof · cited by 10
- InnerProductSpace.HarmonicContOnCl.subproof · cited by 3
- exists_ratio_hasDerivAt_eq_ratio_slopeproof · cited by 3
- intervalIntegral.sub_le_integral_of_hasDeriv_right_of_leproof · cited by 2
- Real.lt_tanproof · cited by 2
- intervalIntegral.intervalIntegrable_log'proof · cited by 2
- norm_image_sub_le_of_norm_deriv_right_le_segmentproof · cited by 2
- image_le_of_liminf_slope_right_le_deriv_boundaryproof · cited by 2
- Complex.circleIntegral_eq_zero_of_differentiable_on_off_countableproof · cited by 2
- intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le_Icoproof · cited by 1