Theorems · Theorem · ring theory
mul_add_one
∀ {α : Type u} [inst : Add α] [inst_1 : MulOneClass α] [LeftDistribClass α] (a b : α), a * (b + 1) = a * b + a- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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
- MulOneClassstatement and proof · cited by 1,018
- mul_addproof · cited by 413
- LeftDistribClassstatement and proof · cited by 12
Cited by19
Results whose statement or proof uses this declaration.
- Ordinal.isNormal_mul_rightproof · cited by 14
- Ordinal.mul_succproof · cited by 8
- ONote.fundamentalSequence_has_propproof · cited by 5
- Ordinal.opow_mulproof · cited by 4
- CliffordAlgebra.map_mul_map_of_isOrtho_of_mem_evenOddproof · cited by 3
- Ordinal.opow_mul_add_lt_opow_mulproof · cited by 2
- Order.height_le_of_krullDim_preimage_leproof · cited by 2
- Ideal.mem_jacobson_iffproof · cited by 2
- Ordinal.log_opow_mul_addproof · cited by 2
- Finpartition.IsEquipartition.exists_partPreservingEquivproof · cited by 1
- Int.mul_lt_floorproof · cited by 1
- Ordinal.IsPrincipal.mul_natCast_ltproof · cited by 1