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15 set "baseuri" "cic:/matita/tests/coercions/".
18 inductive pos: Set \def
22 inductive nat:Set \def
26 inductive int: Set \def
27 | positive: nat \to int
28 | negative : nat \to int.
30 inductive empty : Set \def .
32 let rec pos2nat x \def
34 [ one \Rightarrow (S O)
35 | (next z) \Rightarrow S (pos2nat z)].
37 definition nat2int \def \lambda x. positive x.
43 definition fst \def \lambda x,y:int.x.
45 theorem a: fst O one = fst (positive O) (next one).