alias symbol "pi1" = "exT \fst".
alias symbol "N" = "ordered set N".
+alias symbol "dependent_pair" = "dependent pair".
lemma increasing_supremum_stabilizes:
∀sg:‡ℕ.∀a:sequence {[sg]}.
a is_increasing →
apply (trans_le ??? (le_S_S ?? H8)); rewrite > plus_n_Sm;
apply (le_plus ???? (le_n ?) H9);]]]]
clearbody m; unfold spec in m; clear spec;
+alias symbol "exists" = "CProp exists".
letin find ≝ (
let rec find i u on u : nat ≝
match u with