Theorems · Theorem · group theory
sub_add
∀ {α : Type u_1} [inst : SubtractionCommMonoid α] (a b c : α), a - b + c = a - (b - c)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- SubtractionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_commproof · cited by 1,535
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- neg_add_revproof · cited by 236
- SubtractionCommMonoidstatement and proof · cited by 79
- add_left_commproof · cited by 76
Cited by51
Results whose statement or proof uses this declaration.
- add_sub_sub_cancelproof · cited by 14
- Real.volume_ballproof · cited by 6
- Real.Icc_eq_closedBallproof · cited by 6
- IntervalIntegrable.comp_add_rightproof · cited by 6
- toIocDiv_add_zsmul'proof · cited by 5
- Real.volume_closedBallproof · cited by 5
- toIcoDiv_add_zsmul'proof · cited by 5
- toIocMod_add_zsmul'proof · cited by 5
- toIcoMod_add_zsmul'proof · cited by 5
- descPochhammer_eval_eq_ascPochhammerproof · cited by 4
- Real.sin_ltproof · cited by 4
- Ideal.Quotient.maximal_of_isFieldproof · cited by 4