int_seg	Def {i..j} == {k:| i k < j} Thm* m,n:. {m..n} Type
one_one_corr	Def A ~ B == f:(AB), g:(BA). InvFuns(A; B; f; g) Thm* (A ~ B) Prop
decidable	Def Dec(P) == P P Thm* Dec(A) Prop
equiv_rel	Def compound 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* E:(TTProp). (EquivRel x,y:T. E(x,y)) Prop
int_upper	Def {i...} == {j:| ij} Thm* n:. {n...} Type
lelt	Def i j < k == ij & j < k
inv_funs	Def InvFuns(A; B; f; g) == g o f = Id & f o g = Id Thm* f:(AB), g:(BA). InvFuns(A; B; f; g) Prop
le	Def AB == B < A Thm* i,j:. ij Prop
not	Def A == A False Thm* (A) Prop
trans	Def basic Trans x,y:T. E(x;y) == a,b,c:T. E(a;b) E(b;c) E(a;c) Thm* E:(TTProp). Trans x,y:T. E(x,y) Prop
sym	Def basic Sym x,y:T. E(x;y) == a,b:T. E(a;b) E(b;a) Thm* E:(TTProp). Sym x,y:T. E(x,y) Prop
refl	Def basic Refl(T;x,y.E(x;y)) == a:T. E(a;a) Thm* E:(TTProp). Refl(T;x,y.E(x,y)) Prop
tidentity	Def Id == Id Thm* Id AA
compose	Def (f o g)(x) == f(g(x)) Thm* f:(BC), g:(AB). f o g AC
identity	Def Id(x) == x Thm* Id AA