Theorems · Theorem · combinatorics
List.Vector.head_cons
∀ {α : Type u_1} {n : ℕ} (a : α) (v : List.Vector α n), (a ::ᵥ v).head = aThe head of a vector obtained by prepending is the element prepended.
- Defined in
- Mathlib.Data.Vector.Defs
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
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.
- List.Vectorstatement and proof · cited by 270
- List.Vector.consstatement and proof · cited by 90
- List.Vector.headstatement and proof · cited by 39
Cited by25
Results whose statement or proof uses this declaration.
- Nat.Primrec'.comp₂proof · cited by 8
- Nat.Primrec'.mulproof · cited by 4
- Nat.Primrec'.prec'proof · cited by 4
- Nat.Primrec'.of_primproof · cited by 3
- Nat.Primrec'.predproof · cited by 3
- Nat.Primrec'.subproof · cited by 3
- List.Vector.toList_singletonproof · cited by 2
- List.Vector.get_cons_zeroproof · cited by 2
- Nat.Primrec'.addproof · cited by 2
- Nat.Partrec'.comp₁proof · cited by 2
- Nat.Primrec'.consproof · cited by 2
- Nat.Partrec'.of_partproof · cited by 2