Theorems · Theorem · ring theory
mul_two
∀ {α : Type u} [inst : NonAssocSemiring α] (n : α), n * 2 = n + n- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- NonAssocSemiringstatement and proof · cited by 805
- one_add_one_eq_twoproof · cited by 65
- left_distribproof · cited by 19
Cited by43
Results whose statement or proof uses this declaration.
- add_self_div_twoproof · cited by 18
- continuous_edistproof · cited by 9
- Real.cosh_eqproof · cited by 5
- EuclideanGeometry.dist_smul_vadd_eq_distproof · cited by 4
- LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_ltproof · cited by 3
- Orientation.oangle_eq_of_angle_eq_of_sign_eqproof · cited by 3
- half_lt_self_iffproof · cited by 3
- EulerSine.integral_cos_pow_eqproof · cited by 2
- add_div_two_lt_rightproof · cited by 2
- ZMod.add_self_eq_zero_iff_eq_zeroproof · cited by 2
- Cardinal.mk_perm_eq_self_powerproof · cited by 2
- summable_condensed_iff_of_nonnegproof · cited by 2