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
int_seg	Def {i..j} == {k:| i k < j } Thm* m,n:. {m..n} Type
int_upper	Def {i...} == {j:| ij } Thm* n:. {n...} Type
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
lelt	Def i j < k == ij & j < k
le	Def AB == B < A Thm* i,j:. ij Prop
not	Def A == A False Thm* A:Prop. (A) Prop

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