Theorems · Theorem · group theory
AddMonoidHom.mclosure_preimage_le
∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {F : Type u_4}
[inst_2 : FunLike F M N] [mc : AddMonoidHomClass F M N] (f : F) (s : Set N),
AddSubmonoid.closure (⇑f ⁻¹' s) ≤ AddSubmonoid.comap f (AddSubmonoid.closure s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement · cited by 1,178
- SetLike.mem_coeproof · cited by 302
- AddMonoidHomClassstatement and proof · cited by 252
- AddSubmonoid.closurestatement · cited by 224
- AddSubmonoid.subset_closureproof · cited by 63
- AddSubmonoid.comapstatement · cited by 62
- AddSubmonoid.closure_leproof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- star_le_star_iffproof · cited by 6