Theorems · Theorem · order theory
inf_of_le_right
∀ {α : Type u} [inst : SemilatticeInf α] {a b : α}, b ≤ a → a ⊓ b = bAlias of the reverse direction of inf_eq_right.
- Defined in
- Mathlib.Order.Lattice
- Cited by
- 128 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 26 definitions · uses propext
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeInfstatement and proof · cited by 634
- inf_eq_rightproof · cited by 64
Cited by128
Results whose statement or proof uses this declaration.
- LinearMap.ker_eq_botproof · cited by 92
- Monotone.map_minproof · cited by 43
- top_inf_eqproof · cited by 30
- intervalIntegral.integral_congrproof · cited by 18
- LinearMap.ker_eq_bot'proof · cited by 15
- inf_bot_eqproof · cited by 14
- Set.projIcc_of_memproof · cited by 11
- CategoryTheory.GrothendieckTopology.intersection_coveringproof · cited by 11
- Set.uIoc_eq_unionproof · cited by 8
- Monotone.map_infproof · cited by 8
- sdiff_supproof · cited by 7
- Set.uIoc_of_geproof · cited by 6