Theorems · Theorem · order theory
InitialSeg.map_pred
∀ {α : Type u_1} {β : Type u_2} [inst : PartialOrder α] [inst_1 : PartialOrder β] [inst_2 : PredOrder α] [NoMinOrder α]
[inst_4 : PredOrder β] (f : α ≤i β) (a : α), f (Order.pred a) = Order.pred (f a)- Defined in
- Mathlib.Order.SuccPred.InitialSeg
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- PredOrderstatement and proof · cited by 334
- Order.predstatement · cited by 273
- NoMinOrderstatement and proof · cited by 247
- InitialSegstatement and proof · cited by 70
- CovBy.pred_eqproof · cited by 8
- Order.pred_covByproof · cited by 4
- InitialSeg.apply_covBy_apply_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- PrincipalSeg.map_predproof · cited by 0