Theorems · Theorem · order theory
Order.succ_le_succ_iff_of_not_isMax
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a b : α},
¬IsMax a → ¬IsMax b → (Order.succ a ≤ Order.succ b ↔ a ≤ b)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderSuccOrder
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
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- Order.lt_succ_iff_of_not_isMaxproof · cited by 17
- Order.succ_le_iff_of_not_isMaxproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- Order.succ_eq_succ_iff_of_not_isMaxproof · cited by 3