Definition df-pfx 41884

Description: Define an operation which extracts prefixes of words, i.e. subwords starting at the beginning of a word. Definition in section 9.1 of [AhoHopUll] p. 318. "pfx" is used as label fragment. (Contributed by AV, 2-May-2020.)

Assertion

Ref	Expression
df-pfx	⊢ prefix = (𝑠 ∈ V, 𝑙 ∈ ℕ0 ↦ (𝑠 substr ⟨0, 𝑙⟩))

Distinct variable group:   𝑠,𝑙

Detailed syntax breakdown of Definition df-pfx

Step	Hyp	Ref	Expression
1		cpfx 41883	. 2 class prefix
2		vs	. . 3 setvar 𝑠
3		vl	. . 3 setvar 𝑙
4		cvv 3332	. . 3 class V
5		cn0 11476	. . 3 class ℕ0
6	2	cv 1623	. . . 4 class 𝑠
7		cc0 10120	. . . . 5 class 0
8	3	cv 1623	. . . . 5 class 𝑙
9	7, 8	cop 4319	. . . 4 class ⟨0, 𝑙⟩
10		csubstr 13473	. . . 4 class substr
11	6, 9, 10	co 6805	. . 3 class (𝑠 substr ⟨0, 𝑙⟩)
12	2, 3, 4, 5, 11	cmpt2 6807	. 2 class (𝑠 ∈ V, 𝑙 ∈ ℕ0 ↦ (𝑠 substr ⟨0, 𝑙⟩))
13	1, 12	wceq 1624	1 wff prefix = (𝑠 ∈ V, 𝑙 ∈ ℕ0 ↦ (𝑠 substr ⟨0, 𝑙⟩))

This definition is referenced by:  pfxval  41885  pfx00  41886  pfx0  41887  pfxcl  41888