Theorems · Theorem · field theory
IntermediateField.mem_bot
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {x : E},
x ∈ ⊥ ↔ x ∈ Set.range ⇑(algebraMap F E)- Cited by
- 13 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Bot.botstatement · cited by 4,720
- Algebra.algebraMapstatement · cited by 4,706
- Set.rangestatement · cited by 4,705
- IntermediateFieldstatement · cited by 988
Cited by13
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparableproof · cited by 4
- separableClosure.separableClosure_eq_botproof · cited by 3
- InfiniteGalois.fixedField_fixingSubgroupproof · cited by 3
- separableClosure.map_eq_of_separableClosure_eq_botproof · cited by 2
- Subfield.extendScalars_selfproof · cited by 1
- NumberField.IsCMField.complexConj_eq_self_iffproof · cited by 1
- exists_root_adjoin_eq_top_of_isCyclicproof · cited by 1
- Field.isAlgebraic_of_adjoin_eq_adjoinproof · cited by 1
- Algebra.isInvariant_of_isGaloisproof · cited by 0
- algebraicClosure.map_eq_of_algebraicClosure_eq_botproof · cited by 0
- IntermediateField.restrictRestrictAlgEquivMapHom_surjectiveproof · cited by 0
- IsAlgClosed.of_denseRangeproof · cited by 0