The Holy Prophet of Islam prophecised that the Mahdi will fill the earth with justice and equality just as it will be rife with injustice and inequality. This has been narrated in 130 traditions reported by both Shiah and Sunni traditionalists.

The important part to note is that justice would be done during the lifetime of the Mahdi and not in the near or far future.

For the benefit of my readers, a few references for this tradition are given below:
1.   Musnad Ahmed Ibne Hambal, volume 2, page 37
2.   Al Malahim Ibnul Masnaawi, page 42
3.   Al Bayan by Shafa'ei, chapter 1, page 505
4.   Iqdud Dorar, page 62, chapter 4, part 1
5.   Fara'edus Simtayn, volume 2, page 310, tradition 561
6.   Majmu'us Zawaed, volume 2, page 313
7.   Meezanul Etedaal, volume 3, page 97
8.   Al Fusulul Mohimmah, part 12, page 297
9.   Arful Wardi by Suyuti, volume 2, page 57
10. Tafseere' Durrul Mansur by Suyuti, volume 2, page 58
11. Sawaequl Mohreqah by Ibne' Hajar Makki, pg 166, chp 11, part 1
12. Al Uqoolul Mukhtasar, page 5, chapter 1, tradition 8
13. Al Burhan by Muttaqi Hindi, page 79, chapter 1, tradition 21
14. Kanzul Aamaal, volume 14, page 261, tradition 38653
15. Fara'edul Fawaedul Fikr, chapter 3, page 7
16. As'aaful Raghebayn, page 148
17. Nurul Absar by Shiblanji, page 177
18. Yanabiul Mawaddah, chp 85, page 469 and chapter 94, page 487
19. Al Za'ah, page 119
20. Al Atr'ul Wardi, page 69
21. Aqeedah Ahlus Sunnah, page 9
22. Dalaelul Imamah, page 249
23. Ghabate' Tusi, page 111
24. Al Malahim by Sayyed ibn Tawoos, chapter 23, page 165
25. Kashful Ghummah, volume 3, page 261
26. Isbatul Huda (Shaykh Hurre' Aameli), vol 3, pg 502, chp 32, tdn 292
27. Ibid, volume 3, page 574, chapter 32, part 47, tradition 716
28. Ibid, volume 3, page 575, chapter 32, part 49, tradition 723
29. Hilyatul Abrar, volume 2, chapter 56, page 703, tradition 53
30. Ibid, volume 2, chapter 56, page 713, tradition 101
31. Ghayatul Meraam, chapter 161, page 692, tradition 5
32. Ibid, chapter 161, page 700, tradition 89
33. Ibid, chapter 161, page 703, tradition 137
34. Beharul Anwar, volume 51, chapter 1, page 76, tradition 23-26
35. Ibid, volume 51, page 81
36. Ibid, volume 51, page 92
37. Muntakhabul Asar, chapter 1, part 2, page 169, tradition 70
38. Ibid, chapter 1, part 2, page 170, tradition 77

Leave alone the world, Mirza Ali Mohammed Shirazi, The Bab was unable to establish justice in his own birthplace of iran. If justice was established during the time of the Bab, then why are the Bahais crying themselves hoarse over the injustice meted out to them in Iran.

The Babis themselves perpetrated injustice through the wars fought against the government of Iran in which they killed thousands of innocent children and women. Babis advocated violence and by Babi law were required to kill non-Babis. This has been reported by none other than Mirza Jani, the author of Nuktatul Qaf - the earliest history written about the Babis.