Theorems · Theorem · commutative algebra
Subsemiring.map_le_iff_le_comap
∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] {f : R →+* S} {s : Subsemiring R}
{t : Subsemiring S}, Subsemiring.map f s ≤ t ↔ s ≤ Subsemiring.comap f t- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- Set.image_subset_iffproof · cited by 203
- Subsemiring.mapstatement · cited by 29
- Subsemiring.comapstatement · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- Subsemiring.gc_map_comapproof · cited by 7