Theorems · Theorem · order theory
eq_of_le_of_forall_lt_imp_le_of_dense
∀ {α : Type u_2} [inst : LinearOrder α] [DenselyOrdered α] {a₁ a₂ : α}, a₂ ≤ a₁ → (∀ (a : α), a₂ < a → a₁ ≤ a) → a₁ = a₂- Defined in
- Mathlib.Order.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- LinearOrderDenselyOrdered
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- le_antisymmproof · cited by 2,068
- DenselyOrderedstatement and proof · cited by 471
- le_of_forall_gt_imp_ge_of_denseproof · cited by 21
Cited by4
Results whose statement or proof uses this declaration.
- CauSeq.const_limZeroproof · cited by 6
- eq_of_forall_dist_leproof · cited by 1
- Real.of_nearproof · cited by 0
- eq_of_forall_edist_leproof · cited by 0