Theorems · Theorem · group theory
AddCommute.neg_add_eq_neg_add_iff_of_isAddUnit
∀ {M : Type u_1} [inst : SubtractionMonoid M] {a b c d : M},
AddCommute b d → IsAddUnit b → IsAddUnit d → (-b + a = -d + c ↔ d + a = b + c)- Defined in
- Mathlib.Algebra.Group.Commute.Units
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- SubtractionMonoid
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- add_assocproof · cited by 746
- IsAddUnitstatement and proof · cited by 215
- SubtractionMonoidstatement and proof · cited by 208
- AddCommutestatement and proof · cited by 185
- AddCommute.symmproof · cited by 18
- IsAddUnit.addproof · cited by 11
- IsAddUnit.add_right_injproof · cited by 7
- IsAddUnit.add_neg_cancelproof · cited by 5
- AddCommute.left_commproof · cited by 3
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