This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Value of the prefix extractor as function with domain. (Contributed by AV, 2-May-2020)
|
|
Ref |
Expression |
|
Assertion |
pfxfn |
⊢ ( ( 𝑆 ∈ Word 𝑉 ∧ 𝐿 ∈ ( 0 ... ( ♯ ‘ 𝑆 ) ) ) → ( 𝑆 prefix 𝐿 ) Fn ( 0 ..^ 𝐿 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pfxf |
⊢ ( ( 𝑆 ∈ Word 𝑉 ∧ 𝐿 ∈ ( 0 ... ( ♯ ‘ 𝑆 ) ) ) → ( 𝑆 prefix 𝐿 ) : ( 0 ..^ 𝐿 ) ⟶ 𝑉 ) |
| 2 |
1
|
ffnd |
⊢ ( ( 𝑆 ∈ Word 𝑉 ∧ 𝐿 ∈ ( 0 ... ( ♯ ‘ 𝑆 ) ) ) → ( 𝑆 prefix 𝐿 ) Fn ( 0 ..^ 𝐿 ) ) |