Theorems · Theorem · order theory
not_le_of_gt
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a < b → ¬b ≤ a- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 97 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 11 definitions · uses no axioms
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- lt_iff_le_not_geproof · cited by 35
Cited by97
Results whose statement or proof uses this declaration.
- lt_of_lt_of_leproof · cited by 438
- lt_of_le_of_ltproof · cited by 432
- LT.lt.not_geproof · cited by 305
- lt_irreflproof · cited by 190
- not_lt_of_geproof · cited by 52
- Complex.exp_zeroproof · cited by 43
- Nat.minFac_primeproof · cited by 31
- lt_iff_not_geproof · cited by 22
- Polynomial.coeff_eq_zero_of_degree_ltproof · cited by 22
- lt_of_lt_of_le'proof · cited by 15
- Polynomial.div_modByMonic_uniqueproof · cited by 12
- lt_of_le_of_lt'proof · cited by 11