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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/arity/defs".
19 include "leq/defs.ma".
21 include "getl/defs.ma".
23 inductive arity (g: G): C \to (T \to (A \to Prop)) \def
24 | arity_sort: \forall (c: C).(\forall (n: nat).(arity g c (TSort n) (ASort O
26 | arity_abbr: \forall (c: C).(\forall (d: C).(\forall (u: T).(\forall (i:
27 nat).((getl i c (CHead d (Bind Abbr) u)) \to (\forall (a: A).((arity g d u a)
28 \to (arity g c (TLRef i) a)))))))
29 | arity_abst: \forall (c: C).(\forall (d: C).(\forall (u: T).(\forall (i:
30 nat).((getl i c (CHead d (Bind Abst) u)) \to (\forall (a: A).((arity g d u
31 (asucc g a)) \to (arity g c (TLRef i) a)))))))
32 | arity_bind: \forall (b: B).((not (eq B b Abst)) \to (\forall (c:
33 C).(\forall (u: T).(\forall (a1: A).((arity g c u a1) \to (\forall (t:
34 T).(\forall (a2: A).((arity g (CHead c (Bind b) u) t a2) \to (arity g c
35 (THead (Bind b) u t) a2)))))))))
36 | arity_head: \forall (c: C).(\forall (u: T).(\forall (a1: A).((arity g c u
37 (asucc g a1)) \to (\forall (t: T).(\forall (a2: A).((arity g (CHead c (Bind
38 Abst) u) t a2) \to (arity g c (THead (Bind Abst) u t) (AHead a1 a2))))))))
39 | arity_appl: \forall (c: C).(\forall (u: T).(\forall (a1: A).((arity g c u
40 a1) \to (\forall (t: T).(\forall (a2: A).((arity g c t (AHead a1 a2)) \to
41 (arity g c (THead (Flat Appl) u t) a2)))))))
42 | arity_cast: \forall (c: C).(\forall (u: T).(\forall (a: A).((arity g c u
43 (asucc g a)) \to (\forall (t: T).((arity g c t a) \to (arity g c (THead (Flat
45 | arity_repl: \forall (c: C).(\forall (t: T).(\forall (a1: A).((arity g c t
46 a1) \to (\forall (a2: A).((leq g a1 a2) \to (arity g c t a2)))))).