Theorems · Theorem · order theory
LT.lt.le
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a < b → a ≤ bAlias of le_of_lt.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 2,189 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 11 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
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Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by2,210
Results whose statement or proof uses this declaration.
- inv_posproof · cited by 124
- StrictMono.monotoneproof · cited by 118
- abs_of_posproof · cited by 114
- sq_nonnegproof · cited by 106
- Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_posproof · cited by 58
- div_le_div₀proof · cited by 53
- Real.log_posproof · cited by 51
- abs_of_negproof · cited by 39
- Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonnegproof · cited by 29
- Real.sqrt_eq_rpowproof · cited by 25
- Monotone.strictMono_of_injectiveproof · cited by 22
- Complex.norm_cpow_eq_rpow_re_of_posproof · cited by 21
Showing the 200 most cited of 2,210.