Theorems · Theorem · order theory
Minimal.eq_of_ge
∀ {α : Type u_2} {P : α → Prop} {x y : α} [inst : PartialOrder α], Minimal P x → P y → y ≤ x → x = y- Defined in
- Mathlib.Order.Minimal
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- LE.le.antisymmproof · cited by 507
- Minimalstatement and proof · cited by 150
Cited by7
Results whose statement or proof uses this declaration.
- Minimal.eq_of_leproof · cited by 4
- minimal_iff_eqproof · cited by 3
- minimal_iffproof · cited by 2
- IsCompact.extremePoints_nonemptyproof · cited by 2
- Minimal.eq_of_supersetproof · cited by 2
- IsAntichain.minimal_mem_upperClosure_iff_memproof · cited by 1
- IsLeast.minimal_iffproof · cited by 0