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Theorems · Theorem · field theory

IntermediateField.rank_bot

∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E], Module.rank F ↥⊥ = 1
Defined in
Mathlib.FieldTheory.IntermediateField.Adjoin.Basic
Cited by
5 results in Mathlib
Foundations
Depth 121 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.

Subfield.relrank_self · cited by 2Subfield.relrank_selfIntermediateField.rank_bot' · cited by 2IntermediateField.rank_bo…Field.sepDegree_self · cited by 1Field.sepDegree_selfIntermediateField.relrank_bot_left · cited by 1IntermediateField.relrank…IsPurelyInseparable.sepDegree_eq_one · cited by 1IsPurelyInseparable.sepDe…Algebra · cited by 11388AlgebraField · cited by 7404FieldBot.bot · cited by 4720Bot.botCardinal · cited by 2598CardinalIntermediateField · cited by 988IntermediateFieldModule.rank · cited by 496Module.rankIntermediateField.rank_eq_one_iff · cited by 3IntermediateField.rank_eq…IntermediateField.rank_botCITED BYCITES

Cites7

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

Cited by5

Results whose statement or proof uses this declaration.