Theorems · Inductive type · general algebraic systems
LeftCommutative
{α : Sort u} → {β : Sort v} → (α → β → β) → PropLeftCommutative op where op : α → β → β says that op is a left-commutative operation,
i.e. op a₁ (op a₂ b) = op a₂ (op a₁ b).
- Defined in
- Mathlib.Logic.OpClass
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by23
Results whose statement or proof uses this declaration.
- Multiset.foldrstatement and proof · cited by 18
- Finset.sum_disjiUnionproof · cited by 10
- Finset.prod_disjiUnionproof · cited by 6
- Multiset.foldr_consstatement and proof · cited by 4
- LeftCommutative.left_commstatement and proof · cited by 3
- Multiset.foldr_swapstatement and proof · cited by 3
- Multiset.foldr_inductionstatement and proof · cited by 2
- Multiset.foldr_induction'statement and proof · cited by 2
- List.foldr_cons_eq_foldr_applystatement and proof · cited by 2
- Multiset.coe_foldr_swapstatement and proof · cited by 2
- Multiset.foldr_singletonstatement and proof · cited by 1
- Multiset.foldr.congr_simpstatement and proof · cited by 1