Theorems · Theorem · order theory
lt_iff_lt_of_le_iff_le
∀ {α : Type u_2} {β : Type u_5} [inst : LinearOrder α] [inst_1 : LinearOrder β] {a b : α} {c d : β},
(a ≤ b ↔ c ≤ d) → (b < a ↔ d < c)- Defined in
- Mathlib.Order.Basic
- Cited by
- 54 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- LinearOrderLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- not_leproof · cited by 328
Cited by54
Results whose statement or proof uses this declaration.
- le_iff_le_iff_lt_iff_ltproof · cited by 25
- Polynomial.natDegree_pos_iff_degree_posproof · cited by 22
- Real.sqrt_posproof · cited by 16
- lt_tsub_iff_rightproof · cited by 16
- ENNReal.div_lt_iffproof · cited by 10
- Nat.floor_ltproof · cited by 10
- Nat.lt_ceilproof · cited by 10
- Int.floor_ltproof · cited by 7
- GaloisConnection.lt_iff_ltproof · cited by 6
- Int.lt_ceilproof · cited by 6
- lt_tsub_iff_leftproof · cited by 6
- Real.sqrt_lt_sqrt_iffproof · cited by 5