Mathlib Map

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
Assumes
TopologicalSpaceTopologicalSpaceSubContinuousSub

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousOn.fun_sub · cited by 18ContinuousOn.fun_subDiffContOnCl.sub · cited by 10DiffContOnCl.subInnerProductSpace.HarmonicContOnCl.sub · cited by 3HarmonicContOnCl.subexists_ratio_hasDerivAt_eq_ratio_slope · cited by 3exists_ratio_hasDerivAt_e…intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le · cited by 2intervalIntegral.sub_le_i…Real.lt_tan · cited by 2Real.lt_tanintervalIntegral.intervalIntegrable_log' · cited by 2intervalIntegral.interval…norm_image_sub_le_of_norm_deriv_right_le_segment · cited by 2norm_image_sub_le_of_norm…image_le_of_liminf_slope_right_le_deriv_boundary · cited by 2image_le_of_liminf_slope_…Complex.circleIntegral_eq_zero_of_differentiable_on_off_countable · cited by 2Complex.circleIntegral_eq…Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable_of_tendsto · cited by 1Complex.circleIntegral_su…intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le_Ico · cited by 1intervalIntegral.sub_le_i…Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable_aux · cited by 1Complex.circleIntegral_su…continuousOn_taylorWithinEval · cited by 1continuousOn_taylorWithin…Complex.continuousOn_prod_circle_transform_function · cited by 1Complex.continuousOn_prod…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceContinuousOn · cited by 1411ContinuousOnContinuousSub · cited by 48ContinuousSubContinuousWithinAt.sub · cited by 10ContinuousWithinAt.subContinuousOn.subCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.