Theorems · Theorem · group theory
AddCommGroup.modEq_iff_zsmul
∀ {G : Type u_1} [inst : AddCommGroup G] {p a b : G}, a ≡ b [PMOD p] ↔ ∃ m, m • p = b - a- Defined in
- Mathlib.Algebra.Group.ModEq
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext
- Assumes
- AddCommGroup
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.
- AddCommGroupstatement and proof · cited by 12,871
- add_commproof · cited by 1,535
- sub_eq_add_negproof · cited by 1,023
- natCast_zsmulproof · cited by 118
- AddCommGroup.ModEqstatement · cited by 107
- sub_zsmulproof · cited by 12
- AddCommGroup.modEq_iff_nsmulproof · cited by 11
- sub_eq_sub_iff_add_eq_addproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- AddCommGroup.zsmul_add_modEqproof · cited by 1
- AddCommGroup.add_zsmul_modEqproof · cited by 1
- AddCommGroup.zsmul_modEq_zeroproof · cited by 0
- AddCommGroup.ModEq.zsmulproof · cited by 0
- AddCommGroup.ModEq.of_zsmulproof · cited by 0