Theorems · Theorem · order theory
lt_of_not_ge
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, ¬b ≤ a → a < b- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 374 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 20 definitions · uses no axioms
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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_of_not_geproof · cited by 72
- lt_of_le_not_geproof · cited by 33
Cited by374
Results whose statement or proof uses this declaration.
- lt_or_geproof · cited by 182
- Real.two_pi_posproof · cited by 51
- lt_iff_not_geproof · cited by 22
- lt_imp_lt_of_le_imp_leproof · cited by 18
- Real.exp_strictMonoproof · cited by 17
- Monotone.reflect_ltproof · cited by 14
- Real.cos_pos_of_mem_Iooproof · cited by 14
- Nat.finiteMultiplicity_iffproof · cited by 13
- Complex.Gamma_add_oneproof · cited by 12
- Real.sin_pos_of_pos_of_lt_piproof · cited by 11
- Polynomial.degree_pos_of_irreducibleproof · cited by 10
- AnalyticAt.zpowproof · cited by 8
Showing the 200 most cited of 374.