Theorems · Definition · order theory
WithBot.succ
{α : Type u_1} → [inst : Preorder α] → [OrderBot α] → [SuccOrder α] → WithBot α → αThe successor of a : WithBot α as an element of α.
- Defined in
- Mathlib.Order.SuccPred.WithBot
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Bot.botproof · cited by 4,720
- WithBotstatement and proof · cited by 1,498
- OrderBotstatement and proof · cited by 1,055
- Order.succproof · cited by 633
- SuccOrderstatement and proof · cited by 574
- WithBot.recBotCoeproof · cited by 101
Cited by32
Results whose statement or proof uses this declaration.
- Polynomial.coeffListproof · cited by 22
- Polynomial.withBotSucc_degree_eq_natDegree_add_onestatement and proof · cited by 6
- Polynomial.coeffList_eraseLeadstatement and proof · cited by 4
- WithBot.succ_natCaststatement and proof · cited by 4
- PrimeSpectrum.ConstructibleSetData.degBoundproof · cited by 3
- WithBot.succ_coestatement · cited by 2
- Polynomial.signVariations_eq_eraseLead_add_iteproof · cited by 1
- Polynomial.coeffList_Cproof · cited by 1
- Polynomial.coeffList_C_mulproof · cited by 1
- Polynomial.coeffList_monomialproof · cited by 1
- Polynomial.coeffList_negproof · cited by 1
- WithBot.succ_eq_succstatement and proof · cited by 1