Theorems · Theorem · group theory
AddSubmonoid.map_le_map_iff_of_injective
∀ {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},
Function.Injective ⇑f → ∀ {S T : AddSubmonoid M}, AddSubmonoid.map f S ≤ AddSubmonoid.map f T ↔ S ≤ T- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
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Cites8
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
- FunLikestatement and proof · cited by 2,560
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- AddMonoidHomClassstatement and proof · cited by 252
- AddSubmonoid.mapstatement · cited by 99
- GaloisCoinsertion.l_le_l_iffproof · cited by 11
- AddSubmonoid.gciMapComapproof · cited by 9
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