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Definition df-reverse 13103
Description: Define an operation which reverses the order of symbols in a word. (Contributed by Stefan O'Rear, 26-Aug-2015.)
Assertion
Ref Expression
df-reverse reverse = (𝑠 ∈ V ↦ (𝑥 ∈ (0..^(#‘𝑠)) ↦ (𝑠‘(((#‘𝑠) − 1) − 𝑥))))
Distinct variable group:   𝑥,𝑠

Detailed syntax breakdown of Definition df-reverse
StepHypRef Expression
1 creverse 13095 . 2 class reverse
2 vs . . 3 setvar 𝑠
3 cvv 3169 . . 3 class V
4 vx . . . 4 setvar 𝑥
5 cc0 9789 . . . . 5 class 0
62cv 1473 . . . . . 6 class 𝑠
7 chash 12931 . . . . . 6 class #
86, 7cfv 5787 . . . . 5 class (#‘𝑠)
9 cfzo 12286 . . . . 5 class ..^
105, 8, 9co 6524 . . . 4 class (0..^(#‘𝑠))
11 c1 9790 . . . . . . 7 class 1
12 cmin 10114 . . . . . . 7 class
138, 11, 12co 6524 . . . . . 6 class ((#‘𝑠) − 1)
144cv 1473 . . . . . 6 class 𝑥
1513, 14, 12co 6524 . . . . 5 class (((#‘𝑠) − 1) − 𝑥)
1615, 6cfv 5787 . . . 4 class (𝑠‘(((#‘𝑠) − 1) − 𝑥))
174, 10, 16cmpt 4634 . . 3 class (𝑥 ∈ (0..^(#‘𝑠)) ↦ (𝑠‘(((#‘𝑠) − 1) − 𝑥)))
182, 3, 17cmpt 4634 . 2 class (𝑠 ∈ V ↦ (𝑥 ∈ (0..^(#‘𝑠)) ↦ (𝑠‘(((#‘𝑠) − 1) − 𝑥))))
191, 18wceq 1474 1 wff reverse = (𝑠 ∈ V ↦ (𝑥 ∈ (0..^(#‘𝑠)) ↦ (𝑠‘(((#‘𝑠) − 1) − 𝑥))))
Colors of variables: wff setvar class
This definition is referenced by:  revval  13303
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