Ms Tickle has lived as a woman since 2017, including having surgery, taking hormones and telling family and friends of her decision.

"Up until this instance, everybody has treated me as a woman,” Ms Tickle said.

Ms Tickle's lawyer, Georgina Costello, said the "battlelines" had been drawn on whether her client was female.

"The evidence will show that Ms Tickle is a woman,” Ms Costello said.

"She perceives herself as a woman. She presents herself as a woman."

Giggle's barrister, Bridie Nolan, said the court was being called to determine “what is a female”.

"We say sex is biological and gender is a social construct,” Ms Nolan told the court.

Ms Nolan said the legality of sex created a situation similar to that of "Schrödinger's cat", where someone can be thought of as both male and female simultaneously.

"As Schrödinger's thought experiment aptly demonstrates, theory must be anchored in reality," Ms Nolan said.

“Sex is discriminatory. It always has been. It always will be."

The Giggle app was created to give women a safe space, free from patterns of "male online digital violence", Ms Nolan said.

Ms Grover experienced sexual abuse while working as a screenwriter in Hollywood and had undergone trauma therapy, the court was told.

The app offered a range of ways for users to connect, including finding roommates and engaging socially or romantically.

"The vision was to create an online refuge,” Ms Nolan said.

"It would be a place without harassment, mansplaining, d*** pics, stalking, aggression."

The app uses gender detection software to examine a selfie uploaded by the user and rejects applicants deemed to be male.

Ms Tickle was initially admitted but later excluded when a human assessed her photo, the court heard.

Ms Nolan argued the app was not in breach of sex discrimination laws, which allow for "special measures intended to achieve equality".

The app created greater “equality between men and women in public life" by creating a safe space for women online, she said.

Excluding Ms Tickle, who Ms Nolan argued was a man, would constitute a "special measure" under the laws, she said.

Ms Costello labelled Giggle’s arguments “artificial, after-the-fact justifications" for discrimination against transgender women.

Ms Tickle was issued a birth certificate stating she was female a year after undergoing gender-affirming surgery in October 2019.

"Gender is not merely a biological question, it is partly social and partly psychological," Ms Costello said.

"Ms Tickle was assigned male gender at birth but she has changed to being a woman and that fact is clear in this case."

Representatives from the Australian Human Rights Commission, including Sex Discrimination Commissioner Anna Cody, are assisting the court by providing submissions about the "meaning, scope and validity of relevant provisions of the Sex Discrimination Act".

"The commissioner is not a party to the proceeding and has not made submissions about whether Ms Tickle was in fact discriminated against," the commission said in a statement.

It is the first time the Federal Court has heard a case alleging gender identity discrimination.

Supporters for both sides gathered outside court for the start of the proceedings, protesting within metres of each other.

Justice Robert Bromwich said the court would not tolerate any "intimidation or harassment" either within the courtroom or outside.

"I appreciate that the issues from this case give rise to strongly held views and emotions,” he said.

Some members of the public had shown they were "unable or unwilling to tolerate the existence of any view contrary to their own", Justice Bromwich said.

The hearing continues.

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