Theorems · Theorem · order theory
WithTop.le_iff_forall
∀ {α : Type u_1} [inst : LE α] {x y : WithTop α}, y ≤ x ↔ ∀ (a : α), x = ↑a → ∃ b, y = ↑b ∧ b ≤ a- Defined in
- Mathlib.Order.WithBot
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- WithTopstatement and proof · cited by 3,754
- WithTop.somestatement and proof · cited by 1,128
- WithTop.recTopCoeproof · cited by 107
- WithTop.coe_ne_topproof · cited by 43
- IsEmpty.forall_iffproof · cited by 39
- WithTop.coe_injproof · cited by 21
- WithTop.top_ne_coeproof · cited by 15
- WithTop.le_def'proof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- WithTop.le_coe_iffproof · cited by 2
- Finset.min_of_memproof · cited by 1
- WithTop.coe_le_iffproof · cited by 1
- Finset.inf_of_memproof · cited by 0