Theorems · Theorem · group theory
AddCommute.sub_add_sub_comm
∀ {G : Type u_1} [inst : SubtractionMonoid G] {a b c d : G},
AddCommute b d → AddCommute (-b) c → a - b + (c - d) = a + c - (b + d)- Defined in
- Mathlib.Algebra.Group.Commute.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- SubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- sub_eq_add_negproof · cited by 1,023
- neg_add_revproof · cited by 236
- SubtractionMonoidstatement and proof · cited by 208
- AddCommutestatement and proof · cited by 185
- AddCommute.eqproof · cited by 18
- AddCommute.symmproof · cited by 18
- AddCommute.add_add_add_commproof · cited by 3
- AddCommute.neg_negproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddCommute.add_sub_add_commproof · cited by 0