Theorems · Theorem · order theory
Set.mem_Ioc
∀ {α : Type u_1} [inst : Preorder α] {a b x : α}, x ∈ Set.Ioc a b ↔ a < x ∧ x ≤ b- Defined in
- Mathlib.Order.Interval.Set.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- Preorder
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.
Cited by20
Results whose statement or proof uses this declaration.
- existsUnique_add_zsmul_mem_Iocproof · cited by 7
- Set.Ioo_succ_right_eq_Ioc_of_not_isMaxproof · cited by 4
- Set.Ioc_pred_left_eq_Icc_of_not_isMinproof · cited by 3
- Set.Ioc_pred_right_eq_Iooproof · cited by 3
- Set.Icc_succ_left_eq_Ioc_of_not_isMaxproof · cited by 3
- Real.Angle.nsmul_toReal_eq_mulproof · cited by 2
- Real.Angle.toReal_coe_eq_self_iff_mem_Iocproof · cited by 2
- Real.Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iffproof · cited by 2
- toIocDiv_eq_neg_floorproof · cited by 2
- Rat.finite_rat_abs_sub_lt_one_div_den_sqproof · cited by 1
- Complex.approx_Gamma_integral_tendsto_Gamma_integralproof · cited by 1
- toIocMod_le_rightproof · cited by 1