Theorems · Theorem · field theory
trdeg_subsingleton
∀ {R : Type u_2} {A : Type v} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] [Subsingleton R],
Algebra.trdeg R A = 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemproof · cited by 7,166
- Cardinalstatement · cited by 2,598
- Nat.cast_oneproof · cited by 2,501
- LE.le.antisymmproof · cited by 507
- Cardinal.mk_fintypeproof · cited by 81
- Fintype.card_uniqueproof · cited by 59
- ciSup_le'proof · cited by 39
- Algebra.trdegstatement · cited by 39
- Cardinal.bddAbove_of_smallproof · cited by 37
Cited by2
Results whose statement or proof uses this declaration.
- lift_trdeg_le_of_surjectiveproof · cited by 3
- lift_trdeg_le_of_injectiveproof · cited by 2