Theorems · Theorem · group theory
IsAddUnit.sub_eq_sub_iff
∀ {α : Type u} [inst : SubtractionCommMonoid α] {a b c d : α},
IsAddUnit b → IsAddUnit d → (a - b = c - d ↔ a + d = c + b)- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- SubtractionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_assocproof · cited by 746
- IsAddUnitstatement and proof · cited by 215
- add_right_commproof · cited by 85
- SubtractionCommMonoidstatement and proof · cited by 79
- IsAddUnit.addproof · cited by 11
- IsAddUnit.add_left_injproof · cited by 8
- IsAddUnit.sub_add_cancelproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- IsAddUnit.neg_add_eq_neg_add_iffproof · cited by 0
- IsAddUnit.add_neg_eq_add_neg_iffproof · cited by 0