include "nat/le_arith.ma".
include "russell_support.ma".
-inductive cmp_cases (n,m:nat) : CProp ≝
- | cmp_lt : n < m → cmp_cases n m
- | cmp_eq : n = m → cmp_cases n m
- | cmp_gt : m < n → cmp_cases n m.
-
-lemma cmp_nat: ∀n,m.cmp_cases n m.
-intros; generalize in match (nat_compare_to_Prop n m);
-cases (nat_compare n m); intros;
-[constructor 1|constructor 2|constructor 3] assumption;
-qed.
-
alias symbol "pi1" = "exT \fst".
alias symbol "leq" = "natural 'less or equal to'".
lemma nat_dedekind_sigma_complete: