Theorems · Theorem · ring theory
RingHom.pi_apply
∀ {I : Type u} {f : I → Type u_1} {γ : Type u_2} [inst : (i : I) → NonAssocSemiring (f i)] [inst_1 : NonAssocSemiring γ]
(g : (i : I) → γ →+* f i) (x : γ) (b : I), (RingHom.pi g) x b = (g b) x- Defined in
- Mathlib.Algebra.Ring.Pi
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- NonAssocSemiringstatement and proof · cited by 805
- RingHom.pistatement and proof · cited by 26
Cited by12
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.normAtPlace_applyproof · cited by 8
- NumberField.mixedEmbedding.commMap_canonical_eq_mixedproof · cited by 2
- Pi.ker_ringHomproof · cited by 2
- CompleteOrthogonalIdempotents.bijective_piproof · cited by 2
- AlgebraicGeometry.mono_pushoutSection_of_iSup_eqproof · cited by 2
- Ideal.ker_piRingHom_atPrime_eq_of_pureproof · cited by 1
- NumberField.mixedEmbedding.convexBodyLT'_memproof · cited by 1
- NumberField.mixedEmbedding.convexBodyLT_memproof · cited by 1
- OrthogonalIdempotents.surjective_piproof · cited by 1
- NumberField.mixedEmbedding.mixedEmbedding_apply_isComplexproof · cited by 1
- NumberField.mixedEmbedding.mixedEmbedding_apply_isRealproof · cited by 1
- Pi.ringHom_applyproof · cited by 0