Theorems · Theorem · order theory
WithTop.exists_lt_coe
∀ {α : Type u_1} {a : α} [inst : Preorder α] {p : WithTop α → Prop}, (∃ x < ↑a, p x) ↔ ∃ b < a, p ↑b- Defined in
- Mathlib.Order.WithBot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
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.
- Top.topproof · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- WithTopstatement and proof · cited by 3,754
- WithTop.somestatement and proof · cited by 1,128
- WithTop.coe_lt_coeproof · cited by 47
- not_top_ltproof · cited by 17
- WithTop.existsproof · cited by 2
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Results whose statement or proof uses this declaration.
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