Theorems · Theorem · Lie groups
ContinuousOn.fun_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 (fun i => f i - g i) sEta-expanded form of ContinuousOn.sub
- Defined in
- Mathlib.Topology.Algebra.Group.Defs
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 74 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 · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
- ContinuousOnstatement · cited by 1,411
- ContinuousSubstatement · cited by 48
- ContinuousOn.subproof · cited by 21
Cited by18
Results whose statement or proof uses this declaration.
- cfc_subproof · cited by 5
- Real.sin_gt_sub_cubeproof · cited by 2
- Unitary.two_mul_one_sub_le_norm_sub_one_sqproof · cited by 2
- dist_le_of_approx_trajectories_ODE_of_memproof · cited by 2
- continuousOn_herglotzRieszKernel_sphereproof · cited by 2
- Unitary.norm_sub_one_sq_eqproof · cited by 2
- cfcₙ_subproof · cited by 2
- HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn'proof · cited by 2
- MeasureTheory.continuousOn_convolution_right_with_paramproof · cited by 2
- taylor_mean_remainder_lagrangeproof · cited by 1
- CFC.tendsto_cfc_rpow_sub_one_logproof · cited by 1
- CStarAlgebra.directedOn_nonneg_ballproof · cited by 1