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15 set "baseuri" "cic:/matita/tests/simpl/".
18 alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
19 alias id "plus" = "cic:/Coq/Init/Peano/plus.con".
20 alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
21 alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
22 alias id "not" = "cic:/Coq/Init/Logic/not.con".
28 not (x = y) \to not(y = x).
36 theorem t: let f \def \lambda x,y. x y in f (\lambda x.S x) O = S O.
37 intros. simplify. change in \vdash (? ? (? %) ?) with O.
40 theorem X: \forall x:nat. let myplus \def plus x in myplus (S O) = S x.
41 intros. simplify. change in \vdash (? ? (% ?) ?) with plus x.
42 rewrite > plus_comm. reflexivity. qed.
44 theorem R: \forall x:nat. let uno \def x + O in S O + uno = 1 + x.
46 change in \vdash (? ? (? %) ?) with x + O.
47 rewrite > plus_comm. reflexivity. qed.