theory Examples2
imports Examples
begin
interpretation %visible int: partial_order "op \<le> :: [int, int] \<Rightarrow> bool"
rewrites "int.less x y = (x < y)"
proof -
txt \<open>\normalsize The goals are now:
@{subgoals [display]}
The proof that~@{text \<le>} is a partial order is as above.\<close>
show "partial_order (op \<le> :: int \<Rightarrow> int \<Rightarrow> bool)"
by unfold_locales auto
txt \<open>\normalsize The second goal is shown by unfolding the
definition of @{term "partial_order.less"}.\<close>
show "partial_order.less op \<le> x y = (x < y)"
unfolding partial_order.less_def [OF \<open>partial_order (op \<le>)\<close>]
by auto
qed
text \<open>Note that the above proof is not in the context of the
interpreted locale. Hence, the premise of @{text
"partial_order.less_def"} is discharged manually with @{text OF}.
\<close>
end