Theorems · Theorem · field theory
Subfield.map_bot
∀ {K : Type u} {L : Type v} [inst : DivisionRing K] [inst_1 : DivisionRing L] (f : K →+* L), Subfield.map f ⊥ = ⊥- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingDivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Bot.botstatement · cited by 4,720
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement · cited by 303
- GaloisConnection.l_botproof · cited by 63
- Subfield.mapstatement · cited by 30
- Subfield.gc_map_comapproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- ZMod.fieldRange_castHom_eq_botproof · cited by 2
- Subfield.bot_eq_of_charZeroproof · cited by 0
- Subfield.bot_eq_of_zMod_algebraproof · cited by 0