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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1A/A/defs.ma".
19 implied rec lemma A_rect (P: (A \to Type[0])) (f: (\forall (n: nat).(\forall
20 (n0: nat).(P (ASort n n0))))) (f0: (\forall (a: A).((P a) \to (\forall (a0:
21 A).((P a0) \to (P (AHead a a0))))))) (a: A) on a: P a \def match a with
22 [(ASort n n0) \Rightarrow (f n n0) | (AHead a0 a1) \Rightarrow (f0 a0
23 ((A_rect P f f0) a0) a1 ((A_rect P f f0) a1))].
26 \forall (P: ((A \to Prop))).(((\forall (n: nat).(\forall (n0: nat).(P (ASort
27 n n0))))) \to (((\forall (a: A).((P a) \to (\forall (a0: A).((P a0) \to (P
28 (AHead a a0))))))) \to (\forall (a: A).(P a))))
30 \lambda (P: ((A \to Prop))).(A_rect P).