+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-(* This file was automatically generated: do not edit *********************)
-
-include "Basic-1/lift1/defs.ma".
-
-include "Basic-1/lift/fwd.ma".
-
-theorem lift1_sort:
- \forall (n: nat).(\forall (is: PList).(eq T (lift1 is (TSort n)) (TSort n)))
-\def
- \lambda (n: nat).(\lambda (is: PList).(PList_ind (\lambda (p: PList).(eq T
-(lift1 p (TSort n)) (TSort n))) (refl_equal T (TSort n)) (\lambda (n0:
-nat).(\lambda (n1: nat).(\lambda (p: PList).(\lambda (H: (eq T (lift1 p
-(TSort n)) (TSort n))).(eq_ind_r T (TSort n) (\lambda (t: T).(eq T (lift n0
-n1 t) (TSort n))) (refl_equal T (TSort n)) (lift1 p (TSort n)) H))))) is)).
-(* COMMENTS
-Initial nodes: 99
-END *)
-
-theorem lift1_lref:
- \forall (hds: PList).(\forall (i: nat).(eq T (lift1 hds (TLRef i)) (TLRef
-(trans hds i))))
-\def
- \lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall (i: nat).(eq T
-(lift1 p (TLRef i)) (TLRef (trans p i))))) (\lambda (i: nat).(refl_equal T
-(TLRef i))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda
-(H: ((\forall (i: nat).(eq T (lift1 p (TLRef i)) (TLRef (trans p
-i)))))).(\lambda (i: nat).(eq_ind_r T (TLRef (trans p i)) (\lambda (t: T).(eq
-T (lift n n0 t) (TLRef (match (blt (trans p i) n0) with [true \Rightarrow
-(trans p i) | false \Rightarrow (plus (trans p i) n)])))) (refl_equal T
-(TLRef (match (blt (trans p i) n0) with [true \Rightarrow (trans p i) | false
-\Rightarrow (plus (trans p i) n)]))) (lift1 p (TLRef i)) (H i))))))) hds).
-(* COMMENTS
-Initial nodes: 165
-END *)
-
-theorem lift1_bind:
- \forall (b: B).(\forall (hds: PList).(\forall (u: T).(\forall (t: T).(eq T
-(lift1 hds (THead (Bind b) u t)) (THead (Bind b) (lift1 hds u) (lift1 (Ss
-hds) t))))))
-\def
- \lambda (b: B).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall
-(u: T).(\forall (t: T).(eq T (lift1 p (THead (Bind b) u t)) (THead (Bind b)
-(lift1 p u) (lift1 (Ss p) t)))))) (\lambda (u: T).(\lambda (t: T).(refl_equal
-T (THead (Bind b) u t)))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p:
-PList).(\lambda (H: ((\forall (u: T).(\forall (t: T).(eq T (lift1 p (THead
-(Bind b) u t)) (THead (Bind b) (lift1 p u) (lift1 (Ss p) t))))))).(\lambda
-(u: T).(\lambda (t: T).(eq_ind_r T (THead (Bind b) (lift1 p u) (lift1 (Ss p)
-t)) (\lambda (t0: T).(eq T (lift n n0 t0) (THead (Bind b) (lift n n0 (lift1 p
-u)) (lift n (S n0) (lift1 (Ss p) t))))) (eq_ind_r T (THead (Bind b) (lift n
-n0 (lift1 p u)) (lift n (S n0) (lift1 (Ss p) t))) (\lambda (t0: T).(eq T t0
-(THead (Bind b) (lift n n0 (lift1 p u)) (lift n (S n0) (lift1 (Ss p) t)))))
-(refl_equal T (THead (Bind b) (lift n n0 (lift1 p u)) (lift n (S n0) (lift1
-(Ss p) t)))) (lift n n0 (THead (Bind b) (lift1 p u) (lift1 (Ss p) t)))
-(lift_bind b (lift1 p u) (lift1 (Ss p) t) n n0)) (lift1 p (THead (Bind b) u
-t)) (H u t)))))))) hds)).
-(* COMMENTS
-Initial nodes: 379
-END *)
-
-theorem lift1_flat:
- \forall (f: F).(\forall (hds: PList).(\forall (u: T).(\forall (t: T).(eq T
-(lift1 hds (THead (Flat f) u t)) (THead (Flat f) (lift1 hds u) (lift1 hds
-t))))))
-\def
- \lambda (f: F).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall
-(u: T).(\forall (t: T).(eq T (lift1 p (THead (Flat f) u t)) (THead (Flat f)
-(lift1 p u) (lift1 p t)))))) (\lambda (u: T).(\lambda (t: T).(refl_equal T
-(THead (Flat f) u t)))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p:
-PList).(\lambda (H: ((\forall (u: T).(\forall (t: T).(eq T (lift1 p (THead
-(Flat f) u t)) (THead (Flat f) (lift1 p u) (lift1 p t))))))).(\lambda (u:
-T).(\lambda (t: T).(eq_ind_r T (THead (Flat f) (lift1 p u) (lift1 p t))
-(\lambda (t0: T).(eq T (lift n n0 t0) (THead (Flat f) (lift n n0 (lift1 p u))
-(lift n n0 (lift1 p t))))) (eq_ind_r T (THead (Flat f) (lift n n0 (lift1 p
-u)) (lift n n0 (lift1 p t))) (\lambda (t0: T).(eq T t0 (THead (Flat f) (lift
-n n0 (lift1 p u)) (lift n n0 (lift1 p t))))) (refl_equal T (THead (Flat f)
-(lift n n0 (lift1 p u)) (lift n n0 (lift1 p t)))) (lift n n0 (THead (Flat f)
-(lift1 p u) (lift1 p t))) (lift_flat f (lift1 p u) (lift1 p t) n n0)) (lift1
-p (THead (Flat f) u t)) (H u t)))))))) hds)).
-(* COMMENTS
-Initial nodes: 353
-END *)
-
-theorem lift1_cons_tail:
- \forall (t: T).(\forall (h: nat).(\forall (d: nat).(\forall (hds: PList).(eq
-T (lift1 (PConsTail hds h d) t) (lift1 hds (lift h d t))))))
-\def
- \lambda (t: T).(\lambda (h: nat).(\lambda (d: nat).(\lambda (hds:
-PList).(PList_ind (\lambda (p: PList).(eq T (lift1 (PConsTail p h d) t)
-(lift1 p (lift h d t)))) (refl_equal T (lift h d t)) (\lambda (n:
-nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: (eq T (lift1
-(PConsTail p h d) t) (lift1 p (lift h d t)))).(eq_ind_r T (lift1 p (lift h d
-t)) (\lambda (t0: T).(eq T (lift n n0 t0) (lift n n0 (lift1 p (lift h d
-t))))) (refl_equal T (lift n n0 (lift1 p (lift h d t)))) (lift1 (PConsTail p
-h d) t) H))))) hds)))).
-(* COMMENTS
-Initial nodes: 171
-END *)
-
-theorem lifts1_flat:
- \forall (f: F).(\forall (hds: PList).(\forall (t: T).(\forall (ts:
-TList).(eq T (lift1 hds (THeads (Flat f) ts t)) (THeads (Flat f) (lifts1 hds
-ts) (lift1 hds t))))))
-\def
- \lambda (f: F).(\lambda (hds: PList).(\lambda (t: T).(\lambda (ts:
-TList).(TList_ind (\lambda (t0: TList).(eq T (lift1 hds (THeads (Flat f) t0
-t)) (THeads (Flat f) (lifts1 hds t0) (lift1 hds t)))) (refl_equal T (lift1
-hds t)) (\lambda (t0: T).(\lambda (t1: TList).(\lambda (H: (eq T (lift1 hds
-(THeads (Flat f) t1 t)) (THeads (Flat f) (lifts1 hds t1) (lift1 hds
-t)))).(eq_ind_r T (THead (Flat f) (lift1 hds t0) (lift1 hds (THeads (Flat f)
-t1 t))) (\lambda (t2: T).(eq T t2 (THead (Flat f) (lift1 hds t0) (THeads
-(Flat f) (lifts1 hds t1) (lift1 hds t))))) (eq_ind_r T (THeads (Flat f)
-(lifts1 hds t1) (lift1 hds t)) (\lambda (t2: T).(eq T (THead (Flat f) (lift1
-hds t0) t2) (THead (Flat f) (lift1 hds t0) (THeads (Flat f) (lifts1 hds t1)
-(lift1 hds t))))) (refl_equal T (THead (Flat f) (lift1 hds t0) (THeads (Flat
-f) (lifts1 hds t1) (lift1 hds t)))) (lift1 hds (THeads (Flat f) t1 t)) H)
-(lift1 hds (THead (Flat f) t0 (THeads (Flat f) t1 t))) (lift1_flat f hds t0
-(THeads (Flat f) t1 t)))))) ts)))).
-(* COMMENTS
-Initial nodes: 329
-END *)
-
-theorem lifts1_nil:
- \forall (ts: TList).(eq TList (lifts1 PNil ts) ts)
-\def
- \lambda (ts: TList).(TList_ind (\lambda (t: TList).(eq TList (lifts1 PNil t)
-t)) (refl_equal TList TNil) (\lambda (t: T).(\lambda (t0: TList).(\lambda (H:
-(eq TList (lifts1 PNil t0) t0)).(eq_ind_r TList t0 (\lambda (t1: TList).(eq
-TList (TCons t t1) (TCons t t0))) (refl_equal TList (TCons t t0)) (lifts1
-PNil t0) H)))) ts).
-(* COMMENTS
-Initial nodes: 83
-END *)
-
-theorem lifts1_cons:
- \forall (h: nat).(\forall (d: nat).(\forall (hds: PList).(\forall (ts:
-TList).(eq TList (lifts1 (PCons h d hds) ts) (lifts h d (lifts1 hds ts))))))
-\def
- \lambda (h: nat).(\lambda (d: nat).(\lambda (hds: PList).(\lambda (ts:
-TList).(TList_ind (\lambda (t: TList).(eq TList (lifts1 (PCons h d hds) t)
-(lifts h d (lifts1 hds t)))) (refl_equal TList TNil) (\lambda (t: T).(\lambda
-(t0: TList).(\lambda (H: (eq TList (lifts1 (PCons h d hds) t0) (lifts h d
-(lifts1 hds t0)))).(eq_ind_r TList (lifts h d (lifts1 hds t0)) (\lambda (t1:
-TList).(eq TList (TCons (lift h d (lift1 hds t)) t1) (TCons (lift h d (lift1
-hds t)) (lifts h d (lifts1 hds t0))))) (refl_equal TList (TCons (lift h d
-(lift1 hds t)) (lifts h d (lifts1 hds t0)))) (lifts1 (PCons h d hds) t0)
-H)))) ts)))).
-(* COMMENTS
-Initial nodes: 187
-END *)
-
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