Theorems · Theorem · group theory
add_comm_sub
∀ {α : Type u_1} [inst : SubtractionCommMonoid α] (a b c : α), a - b + c = a + (c - b)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 7 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.
Cites4
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
- SubtractionCommMonoidstatement and proof · cited by 79
- add_left_commproof · cited by 76
Cited by7
Results whose statement or proof uses this declaration.
- Ring.descPochhammer_eq_factorial_smul_chooseproof · cited by 8
- Polynomial.natDegree_preHilbertPolyproof · cited by 3
- vadd_vsub_vadd_commproof · cited by 2
- variationOnFromTo.sub_self_monotoneOnproof · cited by 1
- IsAddUnit.add_eq_add_of_sub_eq_subproof · cited by 0
- NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_topproof · cited by 0
- odd_sub_twoproof · cited by 0