Theorems · Theorem · linear algebra

LinearMap.eqOn_eqLocus

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_3} {M₂ : Type u_4} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
  {f g : M →ₛₗ[τ₁₂] M₂}, Set.EqOn ⇑f ⇑g ↑(f.eqLocus g)

Defined in: Mathlib.Algebra.Module.Submodule.EqLocus
Cited by: 1 results in Mathlib
Foundations: Depth 25 from the axioms · uses propext
Assumes: Semiring Semiring AddCommMonoid AddCommMonoid Module Module

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Cites10

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

DFunLike.coestatement · cited by 62,936
Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
LinearMapstatement and proof · cited by 10,215
RingHomstatement and proof · cited by 10,189
SetLike.coestatement and proof · cited by 8,199
Submodulestatement · cited by 7,192
Set.EqOnstatement · cited by 603
LinearMap.eqLocusstatement and proof · cited by 22

Cited by1

Results whose statement or proof uses this declaration.

ContinuousLinearMap.isStrictMap_isClosed_range_iff_of_finiteRangeSetoidproof · cited by 1