Theorems · Theorem · order theory
OrderIso.map_inf
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : SemilatticeInf β] (f : α ≃o β) (x y : α),
f (x ⊓ y) = f x ⊓ f y- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeInfSemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- OrderIsostatement and proof · cited by 874
- SemilatticeInfstatement and proof · cited by 634
- LE.le.antisymmproof · cited by 507
- OrderIso.symmproof · cited by 475
- OrderIso.symm_apply_applyproof · cited by 41
- OrderIso.le_iff_leproof · cited by 29
- OrderIso.toOrderEmbeddingproof · cited by 22
- OrderEmbedding.map_inf_leproof · cited by 1
Cited by17
Results whose statement or proof uses this declaration.
- neg_infproof · cited by 4
- inv_infproof · cited by 3
- Disjoint.map_orderIsoproof · cited by 3
- inf_mulproof · cited by 2
- mul_inf₀proof · cited by 2
- inf_addproof · cited by 2
- inf_mul₀proof · cited by 1
- mul_infproof · cited by 1
- sub_infproof · cited by 1
- add_infproof · cited by 1
- div_infproof · cited by 1
- inf_divproof · cited by 0