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Theorems · Theorem

Function.LeftInverse.surjective

∀ {α : Sort u_1} {β : Sort u_2} {f : α → β} {g : β → α}, Function.LeftInverse f g → Function.Surjective f
Defined in
Mathlib.Logic.Function.Basic
Cited by
22 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
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Around this declaration

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

GaloisCoinsertion.u_surjective · cited by 10GaloisCoinsertion.u_surje…GaloisInsertion.l_surjective · cited by 9GaloisInsertion.l_surject…Function.invFun_surjective · cited by 8Function.invFun_surjectiveDirectSum.Decomposition.isInternal · cited by 6Decomposition.isInternalMonoid.Coprod.swap_surjective · cited by 3Coprod.swap_surjectiveContinuousLinearMap.isTopCompl_range_ker_of_leftInverse · cited by 3ContinuousLinearMap.isTop…AddMonoid.Coprod.swap_surjective · cited by 3Coprod.swap_surjectiveModule.Invertible.rightInverse_of_leftInverse · cited by 2Invertible.rightInverse_o…Prod.swap_surjective · cited by 1Prod.swap_surjectiveModule.finitePresentation_of_split_exact · cited by 1Module.finitePresentation…Real.sinh_surjective · cited by 1Real.sinh_surjectiveCommRingCat.HomTopology.isClosedEmbedding_hom · cited by 0HomTopology.isClosedEmbed…Monoid.Coprod.snd_surjective · cited by 0Coprod.snd_surjectiveMonoid.Coprod.fst_surjective · cited by 0Coprod.fst_surjectiveConcept.surjective_ofAttributes · cited by 0Concept.surjective_ofAttr…Function.LeftInverse.rightInverse · cited by 2LeftInverse.rightInverseLeftInverse.surjectiveCITED BYCITES

Cites1

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Cited by22

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