Theorems · Definition · order theory
Minimal
{α : Type u_1} → [LE α] → (α → Prop) → α → PropMinimal P x means that x is a minimal element satisfying P.
- Defined in
- Mathlib.Order.Defs.Unbundled
- Cited by
- 150 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by158
Results whose statement or proof uses this declaration.
- Matroid.IsCircuitproof · cited by 108
- Minimal.propstatement and proof · cited by 23
- Minimal.le_of_lestatement and proof · cited by 8
- Minimal.eq_of_gestatement and proof · cited by 7
- Ideal.height_eq_zero_iffproof · cited by 5
- Ideal.IsMinimalPrimeproof · cited by 5
- setOfPred_minimal_antichainstatement · cited by 5
- setOfPred_minimal_subsetstatement · cited by 5
- image_monotone_setOfPred_minimalstatement and proof · cited by 5
- minimalPrimes_eq_minimalsstatement and proof · cited by 4
- zorn_supersetstatement · cited by 4
- Minimal.eq_of_lestatement and proof · cited by 4