Theorems · Theorem
Function.surjective_eval
∀ {α : Sort u} {β : α → Sort v} [h : ∀ (a : α), Nonempty (β a)] (a : α), Function.Surjective (Function.eval a)- Defined in
- Mathlib.Logic.Function.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.updateproof · cited by 502
- Nonempty.someproof · cited by 340
- Function.update_selfproof · cited by 201
- Function.evalstatement · cited by 140
Cited by11
Results whose statement or proof uses this declaration.
- LinearMap.proj_surjectiveproof · cited by 2
- Set.range_evalproof · cited by 1
- Algebra.FormallyUnramified.pi_iffproof · cited by 1
- Pi.locallyConnectedSpace_iffproof · cited by 0
- AddMonoid.exponent_piproof · cited by 0
- Pi.locallyPathConnectedSpace_iffproof · cited by 0
- isPrincipalIdealRing_pi_iffproof · cited by 0
- Ideal.map_evalRingHom_piproof · cited by 0
- Algebra.Etale.iff_exists_algEquiv_prodproof · cited by 0
- Algebra.IsFiniteSplit.bijective_algebraMap_quotientproof · cited by 0
- Monoid.exponent_piproof · cited by 0