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4 (* ||A|| A project by Andrea Asperti *)
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19 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
20 alias id "bool" = "cic:/Coq/Init/Datatypes/bool.ind#xpointer(1/1)".
21 alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
23 inductive t0 : Type :=
25 | k0' : bool → bool → t0.
27 theorem injection_test0: ∀n,n',m,m'. k0 n m = k0 n' m' → m = m'.
33 inductive t : Type → Type :=
37 theorem injection_test1: ∀n,n'. k n = k n' → n = n'.
43 inductive tt (A:Type) : Type -> Type :=
44 k1: nat → nat → tt A nat
45 | k2: bool → bool → tt A bool.
47 theorem injection_test2: ∀n,n',m,m'. k1 bool n n' = k1 bool m m' → n' = m'.
53 inductive ttree : Type → Type :=
55 | tnode : ∀A. ttree A → ttree A → ttree A.
57 theorem injection_test4:
58 ∀n,n',m,m'. k1 bool (S n) (S (S m)) = k1 bool (S n') (S (S (S m'))) → m = S m'.