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Definition df-word 13154
 Description: Define the class of words over a set. A word (or sometimes also called a string) is a finite sequence of symbols from a set (alphabet) 𝑆. Definition in section 9.1 of [AhoHopUll] p. 318. The domain is forced so that two words with the same symbols in the same order will be the same. This is sometimes denoted with the Kleene star, although properly speaking that is an operator on languages. (Contributed by FL, 14-Jan-2014.) (Revised by Stefan O'Rear, 14-Aug-2015.) (Revised by Mario Carneiro, 26-Feb-2016.)
Assertion
Ref Expression
df-word Word 𝑆 = {𝑤 ∣ ∃𝑙 ∈ ℕ0 𝑤:(0..^𝑙)⟶𝑆}
Distinct variable group:   𝑤,𝑙,𝑆

Detailed syntax breakdown of Definition df-word
StepHypRef Expression
1 cS . . 3 class 𝑆
21cword 13146 . 2 class Word 𝑆
3 cc0 9815 . . . . . 6 class 0
4 vl . . . . . . 7 setvar 𝑙
54cv 1474 . . . . . 6 class 𝑙
6 cfzo 12334 . . . . . 6 class ..^
73, 5, 6co 6549 . . . . 5 class (0..^𝑙)
8 vw . . . . . 6 setvar 𝑤
98cv 1474 . . . . 5 class 𝑤
107, 1, 9wf 5800 . . . 4 wff 𝑤:(0..^𝑙)⟶𝑆
11 cn0 11169 . . . 4 class 0
1210, 4, 11wrex 2897 . . 3 wff 𝑙 ∈ ℕ0 𝑤:(0..^𝑙)⟶𝑆
1312, 8cab 2596 . 2 class {𝑤 ∣ ∃𝑙 ∈ ℕ0 𝑤:(0..^𝑙)⟶𝑆}
142, 13wceq 1475 1 wff Word 𝑆 = {𝑤 ∣ ∃𝑙 ∈ ℕ0 𝑤:(0..^𝑙)⟶𝑆}
 Colors of variables: wff setvar class This definition is referenced by:  iswrd  13162  wrdval  13163  nfwrd  13188  csbwrdg  13189
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