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Theorems · Theorem · group theory

AddCommGroup.ModEq.sub

∀ {G : Type u_1} [inst : AddCommGroup G] {p a₁ a₂ b₁ b₂ : G},
  a₁ ≡ b₁ [PMOD p] → a₂ ≡ b₂ [PMOD p] → a₁ - a₂ ≡ b₁ - b₂ [PMOD p]

Alias of the reverse direction of AddCommGroup.ModEq.sub_iff_left.

Defined in
Mathlib.Algebra.Group.ModEq
Cited by
2 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Quot.sound
Assumes
AddCommGroup
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Around this declaration

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

AddCommGroup.ModEq.sub_left · cited by 0ModEq.sub_leftAddCommGroup.ModEq.sub_right · cited by 0ModEq.sub_rightAddCommGroup · cited by 12871AddCommGroupAddCommGroup.ModEq · cited by 107AddCommGroup.ModEqAddCommGroup.ModEq.sub_iff_left · cited by 2ModEq.sub_iff_leftModEq.subCITED BYCITES

Cites3

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Cited by2

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