Mathlib Map

Theorems · Theorem · group theory

AddCommGroup.modEq_iff_eq_add_zsmul

∀ {G : Type u_1} [inst : AddCommGroup G] {p a b : G}, a ≡ b [PMOD p] ↔ ∃ z, b = a + z • p
Defined in
Mathlib.Algebra.Group.ModEq
Cited by
4 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Quot.sound
Assumes
AddCommGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddCommGroup.modEq_iff_toIcoMod_eq_left · cited by 3AddCommGroup.modEq_iff_to…AddCommGroup.modEq_iff_toIocMod_eq_right · cited by 2AddCommGroup.modEq_iff_to…AddCommGroup.modEq_zero_iff_eq_zsmul · cited by 0AddCommGroup.modEq_zero_i…AddCommGroup.not_modEq_iff_ne_add_zsmul · cited by 0AddCommGroup.not_modEq_if…AddCommGroup · cited by 12871AddCommGroupAddCommGroup.ModEq · cited by 107AddCommGroup.ModEqAddCommGroup.modEq_iff_eq_add…CITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.