Mathlib Map

Theorems · Theorem

Prod.mk_eq_zero

∀ {M : Type u_3} {N : Type u_4} [inst : Zero M] [inst_1 : Zero N] {x : M} {y : N}, (x, y) = 0 ↔ x = 0 ∧ y = 0
Defined in
Mathlib.Algebra.Notation.Prod
Cited by
9 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext
Assumes
ZeroZero
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Around this declaration

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

Function.support_prodMk · cited by 3Function.support_prodMkQuadraticMap.posDef_prod_iff · cited by 1QuadraticMap.posDef_prod_…AddSubmonoid.bot_prod_bot · cited by 1AddSubmonoid.bot_prod_botAddSubgroup.bot_prod_bot · cited by 1AddSubgroup.bot_prod_botAddMonoidHom.mker_inl · cited by 1AddMonoidHom.mker_inlAddMonoidHom.mker_inr · cited by 1AddMonoidHom.mker_inrfalse_of_nontrivial_of_product_domain · cited by 0false_of_nontrivial_of_pr…AddMonoidHom.ker_prod · cited by 0AddMonoidHom.ker_prodNumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace · cited by 0mixedEmbedding.injective_…Prod.mk_inj · cited by 16Prod.mk_injProd.mk_eq_zeroCITED BYCITES

Cites1

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Cited by9

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