Description: Letterwise operations on a double letter word. (Contributed by Thierry Arnoux, 7-Oct-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | ofs2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-s2 | |
|
2 | df-s2 | |
|
3 | 1 2 | oveq12i | |
4 | simpll | |
|
5 | 4 | s1cld | |
6 | simplr | |
|
7 | 6 | s1cld | |
8 | simprl | |
|
9 | 8 | s1cld | |
10 | simprr | |
|
11 | 10 | s1cld | |
12 | s1len | |
|
13 | s1len | |
|
14 | 12 13 | eqtr4i | |
15 | 14 | a1i | |
16 | s1len | |
|
17 | s1len | |
|
18 | 16 17 | eqtr4i | |
19 | 18 | a1i | |
20 | 5 7 9 11 15 19 | ofccat | |
21 | 3 20 | eqtrid | |
22 | ofs1 | |
|
23 | 4 8 22 | syl2anc | |
24 | ofs1 | |
|
25 | 6 10 24 | syl2anc | |
26 | 23 25 | oveq12d | |
27 | df-s2 | |
|
28 | 26 27 | eqtr4di | |
29 | 21 28 | eqtrd | |