Some definitions of interest.
preserved_by	Def R preserves P == x,y:T. P(x)  (x R y)  P(y)
	Thm* T:Type, P:(TProp), R:(TTProp). R preserves P  Prop
prop_and	Def (P  Q)(L) == P(L) & Q(L)
	Thm* T:Type, P,Q:(TProp). (P  Q)  TProp

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