If she was liar...

If she was liar, then she did not deserve such a saying from the Prophet that Fatimah is a part of me and whoever angers her, angers me. This itself is a clear indication of her infallibility. The purification sentence of the Holy Quran (the last sentence of verse 33:33) is another indication of her infallibility, as Aisha herself testified (See Sahih Muslim, 1980 Edition, Arabic, v4, p1883, Tradition #61).

Hence there is nothing left for the sensible people but to accept the fact that she was unjustly treated, and that she was easy to be branded as a liar by Umar who was willing to let her burn unless the remaining people in her house come out to vote for Abu Bakr.

So logical conclusion from the above traditions in Sahih al-Bukhari and Sahih Muslim is that Fatimah was treated unjustly, and that she was angry at Abu Bakr and Umar, which follows Allah and his prophet are angry at them according the above tradition in Sahih al-Bukhari. The excuse that Abu Bakr used to refuse to pay the right of Fatimah (see Appendix) was against the text of Quran. How can he be the executor of prophet while he does not obey the clear text of Quran?

Abu Bakr claimed that prophet has said: "We prophets do not leave any inheritance, and whatever we leave should go to charity." This is false allegation that he has made up, because prophet can not contradict Quran which in two verses testifies that prophets had heir, and their children inherited from them. Allah says in Quran: "And Solomon (Sulaymaan) inherited from David." (Quran 27:16) While both Sulaymaan and David were prophets and very wealthy. They were kings of their times.

Allah , Exalted, also says: "(Zakariya prayed to Allah by saying)... Grant me a son from yourself, who inherits from me and inherit from the children of Jacob, and make him, O' my Lord, the one with whom you are well-pleased." (Quran 19:5-6). These are examples that prophets left inheritance. In fact, Fatimah (AS) mentioned these verses as her proof for her right, but Abu Bakr refused due to the suggestion of Umar, and they intentionally went against the clear text of Quran.

Historical facts testifies that prophet even had already transferred Fadak (Which was a big and rich piece of land in Hijaz) to Fatimah and it was the property of Fatimah long before the demise of the Prophet. As such, even it was not even the matter of inheritance as claimed by Abu Bakr.