Theorems · Theorem · order theory
Order.IsNormal.exists_map_le_lt_map_succ
∀ {α : Type u_1} [inst : LinearOrder α] [WellFoundedLT α] [inst_2 : SuccOrder α] [NoMaxOrder α] [inst_4 : OrderBot α]
{f : α → α} {x : α}, Order.IsNormal f → f ⊥ ≤ x → ∃ a, f a ≤ x ∧ x < f (Order.succ a)If f : α → α, we can infer one of the hypotheses in
exists_map_le_lt_map_succ_of_exists_ge.
- Defined in
- Mathlib.Order.IsNormal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
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
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- WellFoundedLTstatement and proof · cited by 491
- NoMaxOrderstatement and proof · cited by 340
- Order.IsNormalstatement and proof · cited by 118
- Order.IsNormal.strictMonoproof · cited by 44
- StrictMono.le_applyproof · cited by 32
- Order.IsNormal.exists_map_le_lt_map_succ_of_exists_geproof · cited by 1
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