Theorems · Theorem · group theory
AddCommGroup.ModEq.add_iff_left
∀ {M : Type u_1} [inst : AddCancelCommMonoid M] {a b c d p : M},
a ≡ b [PMOD p] → (a + c ≡ b + d [PMOD p] ↔ c ≡ d [PMOD p])- Defined in
- Mathlib.Algebra.Group.ModEq
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddCancelCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_commproof · cited by 1,535
- add_assocproof · cited by 746
- AddCommGroup.ModEqstatement and proof · cited by 107
- add_right_commproof · cited by 85
- add_add_add_commproof · cited by 56
- AddCancelCommMonoidstatement and proof · cited by 48
- add_nsmulproof · cited by 44
- add_right_cancelproof · cited by 23
- AddCommGroup.modEq_iff_nsmulproof · cited by 11
- AddCommGroup.ModEq.addproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- AddCommGroup.ModEq.add_iff_rightproof · cited by 1
- AddCommGroup.ModEq.add_left_cancelproof · cited by 1
- AddCommGroup.add_modEq_leftproof · cited by 0