Theorems · Theorem · order theory
forall_lt_imp_le_iff_le_of_dense
∀ {α : Type u_2} [inst : LinearOrder α] [DenselyOrdered α] {a₁ a₂ : α}, (∀ a < a₂, a ≤ a₁) ↔ a₂ ≤ a₁- Defined in
- Mathlib.Order.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrderDenselyOrdered
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- LT.lt.leproof · cited by 2,189
- DenselyOrderedstatement and proof · cited by 471
- LE.le.trans'proof · cited by 140
- le_of_forall_lt_imp_le_of_denseproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- WithTop.ge_of_forall_gt_iff_geproof · cited by 0