Theorems · Theorem · order theory
StrictAnti.le_iff_ge
∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : Preorder β] {f : α → β},
StrictAnti f → ∀ {a b : α}, f a ≤ f b ↔ b ≤ a- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
- Assumes
- LinearOrderPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Preorderstatement and proof · cited by 7,952
- Set.univproof · cited by 3,945
- StrictAntistatement and proof · cited by 204
- StrictAnti.strictAntiOnproof · cited by 16
- StrictAntiOn.le_iff_geproof · cited by 6
Cited by16
Results whose statement or proof uses this declaration.
- EReal.neg_le_neg_iffproof · cited by 9
- ENNReal.inv_le_invproof · cited by 6
- mul_le_mul_right_of_negproof · cited by 2
- zpow_le_zpow_iff_right_of_lt_one₀proof · cited by 2
- Finsupp.DegLex.single_le_iffproof · cited by 1
- StrictAnti.mem_lowerBounds_imageproof · cited by 1
- StrictAnti.mem_upperBounds_imageproof · cited by 1
- pow_le_pow_iff_right_of_lt_one₀proof · cited by 1
- denselyOrdered_iff_of_strictAntiproof · cited by 1
- mul_le_mul_left_of_negproof · cited by 0
- circleIntegrable_sub_zpow_iffproof · cited by 0
- StrictAnti.maximal_of_minimal_imageproof · cited by 0