func string-compare-case-insensitive(x, y) {
      return lower(x) == lower(y) ? lower(x) == lower(y) : lower(x) == lower(y);
    }

/s

More seriously, if you want to learn about this, one place is to look at OpenJDK's sources. E.g. here:

https://github.com/openjdk/jdk/blob/master/src/java.base/sha...

which calls: https://github.com/openjdk/jdk/blob/17283cfe4c697e2118f19992... and https://github.com/openjdk/jdk/blob/17283cfe4c697e2118f19992...