Theorems · Theorem · order theory
pred_notMem_iff_isMin
∀ {α : Type u_3} [inst : PartialOrder α] {s : Set α} [s.OrdConnected] [inst_2 : PredOrder α] [NoMinOrder α] {a : ↑s},
Order.pred ↑a ∉ s ↔ IsMin a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement and proof · cited by 273
- NoMinOrderstatement and proof · cited by 247
- Set.OrdConnectedstatement and proof · cited by 161
- IsMin.pred_eqproof · cited by 6
- coe_pred_of_memproof · cited by 2
- isMin_of_pred_notMemproof · cited by 1
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