Theorems · Theorem · order theory
one_half_lt_one
∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α], 1 / 2 < 1- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- zero_lt_oneproof · cited by 598
- Semifieldstatement and proof · cited by 439
- PosMulReflectLTstatement and proof · cited by 278
- half_lt_selfproof · cited by 38
Cited by12
Results whose statement or proof uses this declaration.
- hasSum_geometric_two'proof · cited by 4
- Asymptotics.IsLittleO.right_isBigO_addproof · cited by 3
- two_inv_lt_oneproof · cited by 3
- Complex.norm_log_one_add_half_le_selfproof · cited by 2
- PiNat.exists_disjoint_cylinderproof · cited by 2
- Real.exists_rat_eq_convergent'proof · cited by 1
- Asymptotics.IsLittleO.right_isBigO_subproof · cited by 1
- controlled_closure_of_completeproof · cited by 1
- exists_forall_closed_ball_dist_add_le_two_subproof · cited by 1
- mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTopproof · cited by 0
- hoferproof · cited by 0
- PiNat.isOpen_iff_distproof · cited by 0