Theorems · Theorem · field theory

Field.Emb.Cardinal.strictMono_leastExt

∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E]
  [rank_inf : Fact (Cardinal.aleph0 ≤ Module.rank F E)] [inst_3 : Algebra.IsAlgebraic F E],
  StrictMono (Field.Emb.Cardinal.leastExt F E)

Defined in: Mathlib.FieldTheory.CardinalEmb
Cited by: 2 results in Mathlib
Foundations: Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Fact Algebra.IsAlgebraic

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Cites25

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
Set.ofPredproof · cited by 6,101
Set.imageproof · cited by 5,609
Factstatement and proof · cited by 2,726
Cardinalstatement · cited by 2,598
Set.Iioproof · cited by 1,166
StrictMonostatement · cited by 706
Cardinal.aleph0statement and proof · cited by 521
Module.rankstatement and proof · cited by 496
IntermediateField.adjoinproof · cited by 382

Cited by2

Results whose statement or proof uses this declaration.

Field.Emb.Cardinal.iSup_adjoin_eq_topproof · cited by 1
Field.Emb.Cardinal.adjoin_image_leastExtproof · cited by 1