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15 (* This file was automatically generated: do not edit *********************)
17 include "LambdaDelta-1/subst0/defs.ma".
19 inductive pr0: T \to (T \to Prop) \def
20 | pr0_refl: \forall (t: T).(pr0 t t)
21 | pr0_comp: \forall (u1: T).(\forall (u2: T).((pr0 u1 u2) \to (\forall (t1:
22 T).(\forall (t2: T).((pr0 t1 t2) \to (\forall (k: K).(pr0 (THead k u1 t1)
23 (THead k u2 t2))))))))
24 | pr0_beta: \forall (u: T).(\forall (v1: T).(\forall (v2: T).((pr0 v1 v2) \to
25 (\forall (t1: T).(\forall (t2: T).((pr0 t1 t2) \to (pr0 (THead (Flat Appl) v1
26 (THead (Bind Abst) u t1)) (THead (Bind Abbr) v2 t2))))))))
27 | pr0_upsilon: \forall (b: B).((not (eq B b Abst)) \to (\forall (v1:
28 T).(\forall (v2: T).((pr0 v1 v2) \to (\forall (u1: T).(\forall (u2: T).((pr0
29 u1 u2) \to (\forall (t1: T).(\forall (t2: T).((pr0 t1 t2) \to (pr0 (THead
30 (Flat Appl) v1 (THead (Bind b) u1 t1)) (THead (Bind b) u2 (THead (Flat Appl)
31 (lift (S O) O v2) t2)))))))))))))
32 | pr0_delta: \forall (u1: T).(\forall (u2: T).((pr0 u1 u2) \to (\forall (t1:
33 T).(\forall (t2: T).((pr0 t1 t2) \to (\forall (w: T).((subst0 O u2 t2 w) \to
34 (pr0 (THead (Bind Abbr) u1 t1) (THead (Bind Abbr) u2 w)))))))))
35 | pr0_zeta: \forall (b: B).((not (eq B b Abst)) \to (\forall (t1: T).(\forall
36 (t2: T).((pr0 t1 t2) \to (\forall (u: T).(pr0 (THead (Bind b) u (lift (S O) O
38 | pr0_tau: \forall (t1: T).(\forall (t2: T).((pr0 t1 t2) \to (\forall (u:
39 T).(pr0 (THead (Flat Cast) u t1) t2)))).