I am trying to understand the algorithm of bitcoin.

Let A be a node, and let (…,T_0,T_1,T_2) represents a block chain that A has at some time.

Here, T_i designate a block which was creaed at the time T_i. Meaning that the block T_n was created before the block T_{n+1} was created.

Now, say miners C,D created two different blocks T_3 and T_3’ within 10 minutes. Then, A appends these two blocks to the current block chain and store them separately. Following the above notation, these two chains are (…,T_0,T_1,T_2,T_3) and (…,T_0,T_1,T_2,T_3’).

Now, say E sent F a some bitcoin and made a transaction which is included in the block T_3.

After some time, if the blockchain (…,T_0,T_1,T_2,T_3’) is chosen to be the correct one, the chain (…,T_0,T_1,T_2,T_3) is removed from server. (Actually, at this point, these two separate blockchains do not appear in this way. That is, they would appear like (…,T_0,T_1,T_2,T_3’,T_4’,…,T_n’) and (…,T_0,T_1,T_2,T_3,T_4,…,T_n) because as time passes new blocks are added.

Assume that the transaction that E sent F some bitcoins was not included in any other blocks excpet the block T_3. (This is possible if E sent F very small amount of money, so if this transacation costs really tiny small fee, miners would not choose this transacation to be included in their block).

In this case, if E wants to send some bitcoins to F, does he have to make a transaction all over again?