Theorems · Theorem · order theory
Set.insert_eq_of_mem
∀ {α : Type u_1} {a : α} {s : Set α}, a ∈ s → insert a s = s- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 118 results in Mathlib
- Foundations
- Depth 16 from the axioms, rests on 68 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by118
Results whose statement or proof uses this declaration.
- hasFPowerSeriesWithinOnBall_univproof · cited by 16
- ContDiffOn.ftaylorSeriesWithinproof · cited by 11
- contDiffOn_succ_iff_fderivWithinproof · cited by 8
- HasFPowerSeriesAt.hasStrictFDerivAtproof · cited by 7
- ContDiffWithinAt.contDiffOn'proof · cited by 7
- ContinuousLinearMap.iteratedFDerivWithin_comp_leftproof · cited by 7
- ContDiffAt.eventuallyproof · cited by 7
- ContDiffOn.differentiableOn_iteratedDerivWithinproof · cited by 6
- Set.encard_sdiff_singleton_add_oneproof · cited by 6
- ContDiffWithinAt.isSymmSndFDerivWithinAtproof · cited by 6
- ContDiffAt.hasStrictFDerivAt'proof · cited by 5
- HasFPowerSeriesOnBall.analyticAt_of_memproof · cited by 5