Theorems · Theorem · order theory
LE.le.eq_or_lt
∀ {α : Type u_2} [inst : PartialOrder α] {a b : α}, a ≤ b → a = b ∨ a < bAlias of eq_or_lt_of_le.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 220 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 57 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
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.
- PartialOrderstatement · cited by 6,410
- eq_or_lt_of_leproof · cited by 92
Cited by220
Results whose statement or proof uses this declaration.
- eq_of_le_of_not_ltproof · cited by 28
- eq_top_or_lt_topproof · cited by 24
- tendsto_pow_atTop_nhds_zero_of_lt_oneproof · cited by 18
- Real.rpow_add'proof · cited by 12
- Ordinal.opow_addproof · cited by 9
- monotone_iff_forall_ltproof · cited by 9
- Int.log_of_right_le_oneproof · cited by 8
- gauge_le_of_memproof · cited by 8
- antitone_iff_forall_ltproof · cited by 7
- Function.Periodic.intervalIntegral_add_eqproof · cited by 7
- gauge_smul_of_nonnegproof · cited by 7
- antitoneOn_iff_forall_ltproof · cited by 6
Showing the 200 most cited of 220.