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Theorems · Theorem · category theory

Profinite.NobelingProof.Products.prop_of_isGood

∀ {I : Type u} (C : Set (I → Bool)) [inst : LinearOrder I] {l : Profinite.NobelingProof.Products I} (J : I → Prop)
  [inst_1 : (j : I) → Decidable (J j)],
  Profinite.NobelingProof.Products.isGood (Profinite.NobelingProof.π C J) l → ∀ a ∈ ↑l, J a
Defined in
Mathlib.Topology.Category.Profinite.Nobeling.Basic
Cited by
10 results in Mathlib
Foundations
Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderDecidable

Around this declaration

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

Profinite.NobelingProof.Products.isGood_mono · cited by 4Products.isGood_monoProfinite.NobelingProof.GoodProducts.good_lt_maxProducts · cited by 1GoodProducts.good_lt_maxP…Profinite.NobelingProof.GoodProducts.square_commutes · cited by 1GoodProducts.square_commu…Profinite.NobelingProof.eval_eq_πJ · cited by 1NobelingProof.eval_eq_πJProfinite.NobelingProof.GoodProducts.smaller_mono · cited by 1GoodProducts.smaller_monoProfinite.NobelingProof.Products.limitOrdinal · cited by 1Products.limitOrdinalProfinite.NobelingProof.GoodProducts.injective_sum_to · cited by 0GoodProducts.injective_su…Profinite.NobelingProof.GoodProducts.union · cited by 0GoodProducts.unionProfinite.NobelingProof.GoodProducts.maxTail_isGood · cited by 0GoodProducts.maxTail_isGo…Profinite.NobelingProof.Products.head_lt_ord_of_isGood · cited by 0Products.head_lt_ord_of_i…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Elem · cited by 7166Set.ElemSet.ofPred · cited by 6101Set.ofPredSet.image · cited by 5609Set.imageSubmodule.span · cited by 1504Submodule.spanLocallyConstant · cited by 227LocallyConstantProfinite.NobelingProof.π · cited by 70NobelingProof.πSubmodule.zero_mem · cited by 58Submodule.zero_memProfinite.NobelingProof.Products · cited by 54NobelingProof.ProductsProfinite.NobelingProof.Products.eval · cited by 29Products.evalProfinite.NobelingProof.Products.isGood · cited by 28Products.isGoodLocallyConstant.ext · cited by 23LocallyConstant.extProfinite.NobelingProof.Proj · cited by 23NobelingProof.ProjProducts.prop_of_isGoodCITED BYCITES

Cites17

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Cited by10

Results whose statement or proof uses this declaration.