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Theorems · Theorem

Function.Surjective.piMap

∀ {ι : Sort u_1} {α : ι → Sort u_2} {β : ι → Sort u_3} {f : (i : ι) → α i → β i},
  (∀ (i : ι), Function.Surjective (f i)) → Function.Surjective (Pi.map f)
Defined in
Mathlib.Logic.Function.Basic
Cited by
6 results in Mathlib
Foundations
Depth 11 from the axioms · uses Classical.choice, Quot.sound
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Around this declaration

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

Function.Surjective.comp_left · cited by 7Surjective.comp_leftIsLocalization.surjective_piRingHom_algebraMap_comp_piEvalRingHom · cited by 1IsLocalization.surjective…cantorToHilbert_surjective · cited by 1cantorToHilbert_surjectiveModule.Basis.ext_multilinear · cited by 1Basis.ext_multilinearFunction.Bijective.piMap · cited by 0Bijective.piMapIsOpenQuotientMap.piMap · cited by 0IsOpenQuotientMap.piMapFunction.surjInv · cited by 63Function.surjInvPi.map · cited by 60Pi.mapFunction.rightInverse_surjInv · cited by 11Function.rightInverse_sur…Surjective.piMapCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.