Theorems · Theorem · commutative algebra
RingHom.sclosure_preimage_le
∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] (f : R →+* S) (s : Set S),
Subsemiring.closure (⇑f ⁻¹' s) ≤ Subsemiring.comap f (Subsemiring.closure s)- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- RingHomstatement and proof · cited by 10,189
- Set.preimagestatement and proof · cited by 4,946
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- SetLike.mem_coeproof · cited by 302
- Subsemiring.closurestatement · cited by 53
- Subsemiring.comapstatement · cited by 20
- Subsemiring.subset_closureproof · cited by 13
- Subsemiring.closure_leproof · cited by 12
- Subsemiring.mem_comapproof · cited by 1
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