Theorems · Theorem · order theory
inf_le_inf
∀ {α : Type u} [inst : SemilatticeInf α] {a b c d : α}, b ≤ a → d ≤ c → b ⊓ d ≤ a ⊓ c- Defined in
- Mathlib.Order.Lattice
- Cited by
- 54 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeInfstatement and proof · cited by 634
- le_infproof · cited by 107
- inf_le_of_left_leproof · cited by 17
- inf_le_of_right_leproof · cited by 10
Cited by54
Results whose statement or proof uses this declaration.
- Set.inter_subset_interproof · cited by 66
- inf_le_inf_leftproof · cited by 25
- inf_le_inf_rightproof · cited by 23
- Filter.prod_monoproof · cited by 14
- iInf_inf_eqproof · cited by 12
- min_le_minproof · cited by 11
- AlgebraicGeometry.Scheme.precoverage_monoproof · cited by 7
- Finset.inter_subset_interproof · cited by 4
- iSup_inf_of_monotoneproof · cited by 3
- IsMinFilter.infproof · cited by 3
- Monotone.infproof · cited by 3
- inf_le_bihimpproof · cited by 3