Theorems · Theorem · order theory
Order.pred_eq_iff_isMin
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : PredOrder α] {a : α}, Order.pred a = a ↔ IsMin a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PartialOrderPredOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Eq.geproof · cited by 375
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement and proof · cited by 273
- Order.pred_leproof · cited by 19
- IsMin.eq_of_leproof · cited by 5
- Order.min_of_le_predproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- IsMin.pred_eqproof · cited by 6
- Order.pred_botproof · cited by 3
- strictMonoOn_of_pred_ltproof · cited by 3
- monotoneOn_of_pred_leproof · cited by 3
- WithBot.pred_coe_of_not_isMinproof · cited by 1
- isMin_of_pred_notMemproof · cited by 1
- Order.not_isMax_predproof · cited by 0
- WithBot.pred_coe_of_isMinproof · cited by 0