Theorems · Theorem · group theory
AddGroupExtension.range_inl_eq_ker_rightHom
∀ {N : Type u_1} {E : Type u_2} {G : Type u_3} [inst : AddGroup N] [inst_1 : AddGroup E] [inst_2 : AddGroup G]
(self : AddGroupExtension N E G), self.inl.range = self.rightHom.kerThe range of the inclusion map is equal to the kernel of the projection map.
- Defined in
- Mathlib.GroupTheory.GroupExtension.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHom.kerstatement · cited by 158
- AddMonoidHom.rangestatement · cited by 142
- AddGroupExtensionstatement and proof · cited by 50
- AddGroupExtension.rightHomstatement · cited by 28
- AddGroupExtension.inlstatement · cited by 20
Cited by6
Results whose statement or proof uses this declaration.
- AddGroupExtension.Section.add_add_add_neg_mem_range_inlproof · cited by 1
- AddGroupExtension.Section.add_neg_add_add_mem_range_inlproof · cited by 1
- AddGroupExtension.Section.add_neg_mem_range_inlproof · cited by 1
- AddGroupExtension.rightHom_inlproof · cited by 1
- AddGroupExtension.Section.neg_add_mem_range_inlproof · cited by 1
- AddGroupExtension.quotientRangeInlEquivRightproof · cited by 0