Theorems · Theorem · order theory
WithTop.ge_of_forall_gt_iff_ge
∀ {α : Type u_1} [inst : LinearOrder α] {x y : WithTop α} [DenselyOrdered α] [NoMaxOrder α],
(∀ (z : α), ↑z < x → ↑z ≤ y) ↔ x ≤ y- Defined in
- Mathlib.Order.WithBot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- WithTopstatement and proof · cited by 3,754
- WithTop.somestatement and proof · cited by 1,128
- DenselyOrderedstatement and proof · cited by 471
- le_topproof · cited by 411
- NoMaxOrderstatement and proof · cited by 340
- not_leproof · cited by 328
- top_le_iffproof · cited by 175
- WithTop.recTopCoeproof · cited by 107
- WithTop.coe_le_coeproof · cited by 65
- NoMaxOrder.exists_gtproof · cited by 62
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