rzk-lang / sHoTT

Formalisations for simplicial HoTT and synthetic ∞-categories.
https://rzk-lang.github.io/sHoTT/
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Proposition utilities #104

Closed TashiWalde closed 1 year ago

TashiWalde commented 1 year ago

I couldn't find some basic facts about propositions, so I added them:

1) Every contractible type is a proposition. 2) All parallel paths in a proposition are equal. 3) Proposition induction 4) Given a family over a proposition, the total type is a proposition iff each fiber is a proposition 5) Propositions are closed under retracts and equivalences 6) Added a few "shortcuts" to go directly between some characterizations of propositions which were only linked by a chain of implication.