Theorems · Theorem · ring theory
NonUnitalRingHom.closure_preimage_le
∀ {R : Type u} {S : Type v} [inst : NonUnitalNonAssocRing R] [inst_1 : NonUnitalNonAssocRing S] (f : R →ₙ+* S)
(s : Set S), NonUnitalSubring.closure (⇑f ⁻¹' s) ≤ NonUnitalSubring.comap f (NonUnitalSubring.closure s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 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
- Set.preimagestatement and proof · cited by 4,946
- NonUnitalNonAssocRingstatement and proof · cited by 354
- SetLike.mem_coeproof · cited by 302
- NonUnitalSubringstatement · cited by 185
- NonUnitalRingHomstatement and proof · cited by 157
- NonUnitalSubring.closurestatement · cited by 23
- NonUnitalSubring.comapstatement · cited by 15
- NonUnitalSubring.subset_closureproof · cited by 9
- NonUnitalSubring.closure_leproof · cited by 7
- NonUnitalSubring.mem_comapproof · cited by 2
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