I'm reading Analysis of hashrate-based double-spending where the following assumptions are made (on page 5):
The total hashrate of the honest network and the attacker is constant, say
H. Let the honest network have
pHhashrate while the attacker has
Mining difficulty is constant, and with hashrate
Hthe average time to mine a block is
The author writes that if the honest network and attacker start mining blocks at the same time then the probability that the former (resp. latter) mines a block first is
Now, while it is intuitive to grasp why this should be true, I am unable to prove so.
Any help would be appreciated!