Theorems · Theorem · group theory
Subsemigroup.map_le_map_iff_of_injective
∀ {M : Type u_1} {N : Type u_2} [inst : Mul M] [inst_1 : Mul N] {f : M →ₙ* N},
Function.Injective ⇑f → ∀ {S T : Subsemigroup M}, Subsemigroup.map f S ≤ Subsemigroup.map f T ↔ S ≤ T- Cited by
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- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
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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
- Subsemigroupstatement and proof · cited by 323
- MulHomstatement and proof · cited by 299
- Subsemigroup.mapstatement · cited by 51
- GaloisCoinsertion.l_le_l_iffproof · cited by 11
- Subsemigroup.gciMapComapproof · cited by 9
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