Theorems · Theorem · ring theory
NonUnitalRingHom.sclosure_preimage_le
∀ {R : Type u} {S : Type v} [inst : NonUnitalNonAssocSemiring R] {F : Type u_1} [inst_1 : FunLike F R S]
[inst_2 : NonUnitalNonAssocSemiring S] [inst_3 : NonUnitalRingHomClass F R S] (f : F) (s : Set S),
NonUnitalSubsemiring.closure (⇑f ⁻¹' s) ≤ NonUnitalSubsemiring.comap f (NonUnitalSubsemiring.closure s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- FunLikestatement and proof · cited by 2,560
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- SetLike.mem_coeproof · cited by 302
- NonUnitalSubsemiringstatement · cited by 201
- NonUnitalRingHomClassstatement and proof · cited by 82
- NonUnitalSubsemiring.closurestatement · cited by 31
- NonUnitalSubsemiring.comapstatement · cited by 14
- NonUnitalSubsemiring.subset_closureproof · cited by 10
- NonUnitalSubsemiring.closure_leproof · cited by 8
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