Mathlib Map

Theorems · Theorem · field theory

IntermediateField.sub_mem

∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (S : IntermediateField K L)
  {x y : L}, x ∈ S → y ∈ S → x - y ∈ S

An intermediate field is closed under subtraction.

Defined in
Mathlib.FieldTheory.IntermediateField.Basic
Cited by
2 results in Mathlib
Foundations
Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Field.primitive_element_inf_aux · cited by 1Field.primitive_element_i…Field.isSeparable_sub · cited by 1Field.isSeparable_subAlgebra · cited by 11388AlgebraField · cited by 7404FieldIntermediateField · cited by 988IntermediateFieldsub_mem · cited by 40sub_memIntermediateField.sub_memCITED BYCITES

Cites4

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

Cited by2

Results whose statement or proof uses this declaration.