Theorems · Theorem · field theory
add_halves
∀ {K : Type u_1} [inst : DivisionSemiring K] [NeZero 2] (a : K), a / 2 + a / 2 = a- Defined in
- Mathlib.Algebra.Field.Basic
- Cited by
- 78 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
- Assumes
- DivisionSemiringNeZero
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.
- DivisionSemiringstatement and proof · cited by 216
- add_divproof · cited by 89
- add_self_div_twoproof · cited by 18
Cited by78
Results whose statement or proof uses this declaration.
- Asymptotics.IsLittleO.addproof · cited by 17
- sub_halfproof · cited by 7
- CauSeq.abv_pos_of_not_limZeroproof · cited by 6
- CauSeq.add_limZeroproof · cited by 6
- multipliable_one_add_of_summableproof · cited by 4
- Real.arccos_cosproof · cited by 4
- uniformContinuous_distproof · cited by 4
- Orientation.oangle_add_right_smul_rotation_pi_div_twoproof · cited by 4
- AddCircle.volume_closedBallproof · cited by 4
- rieszContentAux_sup_leproof · cited by 3
- IsCauSeq.cauchy₂proof · cited by 3
- Real.abs_sin_halfproof · cited by 3