Theorems · Theorem
Function.Injective.nontrivial
∀ {α : Type u_1} {β : Type u_2} [Nontrivial α] {f : α → β}, Function.Injective f → Nontrivial βPushforward a Nontrivial instance along an injective function.
- Defined in
- Mathlib.Logic.Nontrivial.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Nontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement and proof · cited by 2,416
- exists_pair_neproof · cited by 32
Cited by17
Results whose statement or proof uses this declaration.
- IsLocalization.rank_eqproof · cited by 7
- AlgebraicIndependent.extendScalarsproof · cited by 4
- Algebra.FormallyUnramified.iff_comp_injective_of_smallproof · cited by 4
- IsBaseChange.lift_rank_eqproof · cited by 3
- Algebra.IsAlgebraic.isDomain_of_adjoin_rangeproof · cited by 2
- lift_trdeg_add_eqproof · cited by 2
- Valuation.Integers.nontrivial_iffproof · cited by 2
- IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiffproof · cited by 2
- HahnEmbedding.Partial.orderTop_eq_iffproof · cited by 1
- IsAlgebraic.adjoin_of_forall_isAlgebraicproof · cited by 1
- exists_isTranscendenceBasis_betweenproof · cited by 1
- AlgebraicIndepOn.insertproof · cited by 1