Theorems · Theorem · group theory
AddSubmonoid.map_bot
∀ {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), AddSubmonoid.map f ⊥ = ⊥- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- FunLikestatement and proof · cited by 2,560
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement · cited by 1,178
- AddMonoidHomClassstatement and proof · cited by 252
- AddSubmonoid.mapstatement · cited by 99
- GaloisConnection.l_botproof · cited by 63
- AddSubmonoid.gc_map_comapproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- AddSubmonoid.closure_prod_zeroproof · cited by 1
- AddSubmonoid.closure_zero_prodproof · cited by 1
- AddSubmonoid.smul_botproof · cited by 0
- AddSubmonoid.disjoint_mapproof · cited by 0