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Theorems · Theorem · field theory

IntermediateField.neg_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 : L}, x ∈ S → -x ∈ S
Defined in
Mathlib.FieldTheory.IntermediateField.Basic
Cited by
2 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebra
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Around this declaration

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

IntermediateField.toSubfield · cited by 38IntermediateField.toSubfi…IntermediateField.sInf_toSubfield · cited by 1IntermediateField.sInf_to…Field.isSeparable_neg · cited by 0Field.isSeparable_negAlgebra · cited by 11388AlgebraField · cited by 7404FieldIntermediateField · cited by 988IntermediateFieldIntermediateField.neg_memCITED BYCITES

Cites3

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Cited by3

Results whose statement or proof uses this declaration.