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Database REAL AND COMPLEX NUMBERS Words over a set Subwords/substrings swrdvalfn
Description: Value of the subword extractor as function with domain. (Contributed by Alexander van der Vekens , 28-Mar-2018) (Proof shortened by AV , 2-May-2020)
Ref
Expression
Assertion
swrdvalfn ⊢ ( ( 𝑆 ∈ Word 𝑉 ∧ 𝐹 ∈ ( 0 ... 𝐿 ) ∧ 𝐿 ∈ ( 0 ... ( ♯ ‘ 𝑆 ) ) ) → ( 𝑆 substr ⟨ 𝐹 , 𝐿 ⟩ ) Fn ( 0 ..^ ( 𝐿 − 𝐹 ) ) )
Proof
Step
Hyp
Ref
Expression
1
swrdf ⊢ ( ( 𝑆 ∈ Word 𝑉 ∧ 𝐹 ∈ ( 0 ... 𝐿 ) ∧ 𝐿 ∈ ( 0 ... ( ♯ ‘ 𝑆 ) ) ) → ( 𝑆 substr ⟨ 𝐹 , 𝐿 ⟩ ) : ( 0 ..^ ( 𝐿 − 𝐹 ) ) ⟶ 𝑉 )
2
1
ffnd ⊢ ( ( 𝑆 ∈ Word 𝑉 ∧ 𝐹 ∈ ( 0 ... 𝐿 ) ∧ 𝐿 ∈ ( 0 ... ( ♯ ‘ 𝑆 ) ) ) → ( 𝑆 substr ⟨ 𝐹 , 𝐿 ⟩ ) Fn ( 0 ..^ ( 𝐿 − 𝐹 ) ) )