Theorems · Theorem · order theory
le_total
∀ {α : Type u_1} [inst : LinearOrder α] (a b : α), a ≤ b ∨ b ≤ a- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 294 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 9 definitions · uses no axioms
- Assumes
- LinearOrder
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
- LinearOrder.le_totalproof · cited by 1
Cited by294
Results whose statement or proof uses this declaration.
- Real.exp_posproof · cited by 169
- abs_mulproof · cited by 98
- le_of_not_geproof · cited by 72
- lt_minproof · cited by 69
- Monotone.map_maxproof · cited by 55
- Monotone.map_minproof · cited by 43
- max_ltproof · cited by 42
- intervalIntegral.integral_congrproof · cited by 18
- Nat.log_zero_rightproof · cited by 18
- Real.arcsin_negproof · cited by 11
- Cardinal.toENat_liftproof · cited by 10
- HasSum.nat_add_negproof · cited by 10
Showing the 200 most cited of 294.