Theorems · Theorem · order theory
Order.pred_lt_iff
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {a b : α} [NoMinOrder α], Order.pred b < a ↔ b ≤ a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- PredOrderstatement and proof · cited by 334
- Order.predstatement · cited by 273
- NoMinOrderstatement and proof · cited by 247
- not_isMinproof · cited by 42
- Order.pred_lt_iff_of_not_isMinproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- Order.pred_lt_iff_eq_or_gtproof · cited by 1
- Order.pred_lt_pred_iffproof · cited by 1
- Order.pred_le_pred_iffproof · cited by 1
- Order.pred_top_lt_iffproof · cited by 0