Theorems · Theorem · ring theory
Algebra.gc
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A],
GaloisConnection (Algebra.adjoin R) SetLike.coe- Cited by
- 7 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- Subalgebrastatement and proof · cited by 1,353
- le_transproof · cited by 985
- Algebra.adjoinstatement and proof · cited by 535
- GaloisConnectionstatement · cited by 253
Cited by8
Results whose statement or proof uses this declaration.
- Algebra.subset_adjoinproof · cited by 109
- Algebra.adjoin_leproof · cited by 36
- Algebra.adjoin_le_iffproof · cited by 26
- Algebra.adjoin_monoproof · cited by 24
- Algebra.adjoin_emptyproof · cited by 10
- Algebra.adjoin_unionproof · cited by 7
- Algebra.giproof · cited by 1
- Algebra.adjoin_iUnionproof · cited by 1