T:Type, R:(T
TProp). Preorder(T;x,y.R(x,y)) 
Propa,b,c:T. E(a;b) 
E(b;c) E(a;c)T:Type, E:(TTProp). (Trans x,y:T. E(x,y)) Propa:T. E(a;a)T:Type, E:(TTProp). Refl(T;x,y.E(x,y)) Prop| Who Cites preorder? | |
| preorder | Def Preorder(T;x,y.R(x;y)) == Refl(T;x,y.R(x;y)) & (Trans x,y:T. R(x;y)) |
| Thm* T:Type, R:(TTProp). Preorder(T;x,y.R(x,y)) Prop | |
| trans | Def Trans x,y:T. E(x;y) == a,b,c:T. E(a;b) E(b;c) E(a;c) |
| Thm* T:Type, E:(TTProp). (Trans x,y:T. E(x,y)) Prop | |
| refl | Def Refl(T;x,y.E(x;y)) == a:T. E(a;a) |
| Thm* T:Type, E:(TTProp). Refl(T;x,y.E(x,y)) Prop |
| Syntax: | Preorder(T;x,y.R(x;y)) | has structure: | preorder(T; x,y.R(x;y)) |
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