equiv_rel	Def EquivRel x,y:T. E(x;y) == Refl(T;x,y.E(x;y)) & Sym x,y:T. E(x;y) & Trans x,y:T. E(x;y) Thm* T:Type, E:(TTProp). (EquivRel x,y:T. E(x,y)) Prop
one_one_corr	Def A ~ B == f:(AB), g:(BA). InvFuns(A; B; f; g) Thm* A,B:Type. (A ~ B) Prop
inv_funs	Def InvFuns(A; B; f; g) == g o f = Id & f o g = Id Thm* A,B:Type, f:(AB), g:(BA). InvFuns(A; B; f; g) 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
sym	Def Sym x,y:T. E(x;y) == a,b:T. E(a;b) E(b;a) Thm* T:Type, E:(TTProp). Sym 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
tidentity	Def Id == Id Thm* A:Type. Id AA
compose	Def (f o g)(x) == f(g(x)) Thm* A,B,C:Type, f:(BC), g:(AB). f o g AC
identity	Def Id(x) == x Thm* A:Type. Id AA

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