Description: The half-open interval expressed using a composition of a function into ( RR X. RR ) and using two distinct real-valued functions for the borders. (Contributed by Glauco Siliprandi, 24-Dec-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | hoi2toco.1 | |
|
hoi2toco.c | |
||
Assertion | hoi2toco | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hoi2toco.1 | |
|
2 | hoi2toco.c | |
|
3 | 2 | funmpt2 | |
4 | 3 | a1i | |
5 | 4 | adantr | |
6 | simpr | |
|
7 | 2 | dmeqi | |
8 | 7 | a1i | |
9 | opex | |
|
10 | 9 | 2a1i | |
11 | 1 10 | ralrimi | |
12 | dmmptg | |
|
13 | 11 12 | syl | |
14 | 8 13 | eqtr2d | |
15 | 14 | adantr | |
16 | 6 15 | eleqtrd | |
17 | fvco | |
|
18 | 5 16 17 | syl2anc | |
19 | 9 | a1i | |
20 | 2 | fvmpt2 | |
21 | 6 19 20 | syl2anc | |
22 | 21 | fveq2d | |
23 | df-ov | |
|
24 | 23 | eqcomi | |
25 | 24 | a1i | |
26 | 18 22 25 | 3eqtrd | |
27 | 1 26 | ixpeq2d | |