To show he lied, you have to prove he intended to deceive and you haven't done that. Instead, you're claiming you know his thoughts. Additionally, you have overlooked the fact that the police did show him the part of his first statement that was relevant to what they were asking him about at the time.
It is not plausible that he forgot that he phoned Julie before police and honestly made an error thinking he called her after calling the police. He knew it would look bad to tell the truth so that was why he lied and said he called police before Julie. Saying that you refuse to believe he lied about it is meaningless and doesn't render it not proven.
He blatantly lied about calling police before Julie, messed up admitting he called Julie first then reverted to his prior claims saying he stood by whatever he put in his statements. He then lied at trial testifying he remembered calling police first.