Theorems · Theorem · order theory
Minimal.le_of_le
∀ {α : Type u_1} [inst : LE α] {P : α → Prop} {x y : α}, Minimal P x → P y → y ≤ x → x ≤ y- Defined in
- Mathlib.Order.Defs.Unbundled
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Minimalstatement and proof · cited by 150
Cited by8
Results whose statement or proof uses this declaration.
- minimal_mem_image_monotoneproof · cited by 3
- minimal_mem_image_monotone_iffproof · cited by 3
- minimal_iff_isMinproof · cited by 2
- minimal_iff_minimal_of_imp_of_forallproof · cited by 2
- Minimal.monoproof · cited by 2
- Finset.minimal_iff_forall_eraseproof · cited by 1
- OrderEmbedding.minimal_apply_mem_inter_range_iffproof · cited by 1
- minimal_minimalproof · cited by 0