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Theorems · Definition · group theory

FreeAddMonoid.length

{α : Type u_1} → FreeAddMonoid α → ℕ

The length of an additive free monoid element: 1.length = 0 and (a + b).length = a.length + b.length

Defined in
Mathlib.Algebra.FreeMonoid.Basic
Cited by
12 results in Mathlib
Foundations
Depth 14 from the axioms · uses Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FreeAddMonoid.of_ne_zero · cited by 2FreeAddMonoid.of_ne_zeroFreeAddMonoid.length_add · cited by 1FreeAddMonoid.length_addFreeAddMonoid.length_eq_zero · cited by 1FreeAddMonoid.length_eq_z…FreeAddMonoid.map_surjective · cited by 0FreeAddMonoid.map_surject…FreeAddMonoid.length_eq_four · cited by 0FreeAddMonoid.length_eq_f…FreeAddMonoid.length_eq_one · cited by 0FreeAddMonoid.length_eq_o…FreeAddMonoid.length_eq_three · cited by 0FreeAddMonoid.length_eq_t…FreeAddMonoid.length_eq_two · cited by 0FreeAddMonoid.length_eq_t…FreeAddMonoid.length_of · cited by 0FreeAddMonoid.length_ofFreeAddMonoid.length_reverse · cited by 0FreeAddMonoid.length_reve…FreeAddMonoid.length_surjective · cited by 0FreeAddMonoid.length_surj…FreeAddMonoid.length_zero · cited by 0FreeAddMonoid.length_zeroDFunLike.coe · cited by 62936DFunLike.coeFreeAddMonoid · cited by 145FreeAddMonoidFreeAddMonoid.toList · cited by 32FreeAddMonoid.toListFreeAddMonoid.lengthCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by12

Results whose statement or proof uses this declaration.