Theorems · Theorem · field theory
perfectField_of_perfectClosure_eq_bot
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [h : PerfectField E], perfectClosure F E = ⊥ → PerfectField F
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Bot.botstatement and proof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- IntermediateFieldstatement · cited by 988
- pow_oneproof · cited by 894
- AlgHom.toRingHomproof · cited by 490
- ExpCharproof · cited by 276
- RingHom.injectiveproof · cited by 187
- Algebra.ofIdproof · cited by 166
- PerfectRingproof · cited by 154
Cited by1
Results whose statement or proof uses this declaration.
- perfectField_of_isSeparable_of_perfectField_topproof · cited by 1