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Theorems · Theorem · group theory

AddCommGroup.map_modEq_iff

∀ {M : Type u_1} [inst : AddCommMonoid M] {a b p : M} {N : Type u_2} {F : Type u_3} [inst_1 : AddCommMonoid N]
  [inst_2 : FunLike F M N] [AddMonoidHomClass F M N] (f : F),
  Function.Injective ⇑f → (f a ≡ f b [PMOD f p] ↔ a ≡ b [PMOD p])
Defined in
Mathlib.Algebra.Group.ModEq
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound
Assumes
AddCommMonoidAddCommMonoidFunLikeAddMonoidHomClass
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Around this declaration

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

AddCommGroup.intCast_modEq_intCast · cited by 3AddCommGroup.intCast_modE…AddCommGroup.natCast_modEq_natCast · cited by 1AddCommGroup.natCast_modE…DFunLike.coe · cited by 62936DFunLike.coeAddCommMonoid · cited by 12281AddCommMonoidFunLike · cited by 2560FunLikeAddMonoidHomClass · cited by 252AddMonoidHomClassAddCommGroup.ModEq · cited by 107AddCommGroup.ModEqAddCommGroup.map_modEq_iffCITED BYCITES

Cites5

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Cited by2

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