X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Flift%2Fprops.ma;h=f0ed224515471af542b1c2c07e16cd6056cb3e4f;hb=d6a9ed2a08fcc4e3e26a40cde8cab88c2c69cb3a;hp=748f9a280b31209a7be85f794186137318e63cdc;hpb=3531d88e2a19cba027b4b882f8dd74bf37283b9c;p=helm.git diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/lift/props.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/lift/props.ma index 748f9a280..f0ed22451 100644 --- a/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/lift/props.ma +++ b/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/lift/props.ma @@ -14,9 +14,9 @@ (* This file was automatically generated: do not edit *********************) -include "LambdaDelta-1/lift/fwd.ma". +include "Basic-1/lift/fwd.ma". -include "LambdaDelta-1/s/props.ma". +include "Basic-1/s/props.ma". theorem thead_x_lift_y_y: \forall (k: K).(\forall (t: T).(\forall (v: T).(\forall (h: nat).(\forall @@ -78,6 +78,9 @@ Prop).P0)))))) H0 k0 H6) in (let H8 \def (eq_ind T (lift h d (THead k0 t0 t1)) (\lambda (t2: T).(eq T t2 t1)) H4 (THead k0 (lift h d t0) (lift h (s k0 d) t1)) (lift_head k0 t0 t1 h d)) in (H7 (lift h d t0) h (s k0 d) H8 P)))))) H3)) H2)))))))))))) t)). +(* COMMENTS +Initial nodes: 887 +END *) theorem lift_r: \forall (t: T).(\forall (d: nat).(eq T (lift O d t) t)) @@ -96,6 +99,9 @@ t1)))).(\lambda (d: nat).(eq_ind_r T (THead k (lift O d t0) (lift O (s k d) t1)) (\lambda (t2: T).(eq T t2 (THead k t0 t1))) (f_equal3 K T T T THead k k (lift O d t0) t0 (lift O (s k d) t1) t1 (refl_equal K k) (H d) (H0 (s k d))) (lift O d (THead k t0 t1)) (lift_head k t0 t1 O d)))))))) t). +(* COMMENTS +Initial nodes: 367 +END *) theorem lift_lref_gt: \forall (d: nat).(\forall (n: nat).((lt d n) \to (eq T (lift (S O) d (TLRef @@ -109,6 +115,9 @@ theorem lift_lref_gt: (lift (S O) d (TLRef (pred n))) (lift_lref_ge (pred n) (S O) d (le_S_n d (pred n) (eq_ind nat n (\lambda (n0: nat).(le (S d) n0)) H (S (pred n)) (S_pred n d H))))))). +(* COMMENTS +Initial nodes: 193 +END *) theorem lifts_tapp: \forall (h: nat).(\forall (d: nat).(\forall (v: T).(\forall (vs: TList).(eq @@ -123,6 +132,9 @@ t0) (lift h d v)) (\lambda (t1: TList).(eq TList (TCons (lift h d t) t1) (TCons (lift h d t) (TApp (lifts h d t0) (lift h d v))))) (refl_equal TList (TCons (lift h d t) (TApp (lifts h d t0) (lift h d v)))) (lifts h d (TApp t0 v)) H)))) vs)))). +(* COMMENTS +Initial nodes: 215 +END *) theorem lift_inj: \forall (x: T).(\forall (t: T).(\forall (h: nat).(\forall (d: nat).((eq T @@ -183,6 +195,9 @@ T).(\lambda (x1: T).(\lambda (H3: (eq T t1 (THead (Flat f) x0 x1))).(\lambda (THead (Flat f) t t0) t2)) (f_equal3 K T T T THead (Flat f) (Flat f) t x0 t0 x1 (refl_equal K (Flat f)) (H x0 h d H4) (H0 x1 h d H5)) t1 H3)))))) (lift_gen_flat f (lift h d t) (lift h d t0) t1 h d H2)))))))))))) k)) x). +(* COMMENTS +Initial nodes: 1391 +END *) theorem lift_gen_lift: \forall (t1: T).(\forall (x: T).(\forall (h1: nat).(\forall (h2: @@ -378,6 +393,9 @@ d2 x3))) (lift h2 d2 (THead (Flat f) x2 x3)) (lift_flat f x2 x3 h2 d2))) t0 H11) x1 H10)))) (H0 x1 h1 h2 d1 d2 H1 H7)) t H9) x0 H8)))) (H x0 h1 h2 d1 d2 H1 H6)) x H5)))))) (lift_gen_flat f (lift h1 d1 t) (lift h1 d1 t0) x h2 (plus d2 h1) H4))))) k H2))))))))))))) t1). +(* COMMENTS +Initial nodes: 5037 +END *) theorem lifts_inj: \forall (xs: TList).(\forall (ts: TList).(\forall (h: nat).(\forall (d: @@ -427,6 +445,9 @@ d t0)) (TCons (lift h d t1) (lifts h d t2)) H1) in (\lambda (H4: (eq T (lift h d t) (lift h d t1))).(eq_ind T t (\lambda (t3: T).(eq TList (TCons t t0) (TCons t3 t2))) (f_equal2 T TList TList TCons t t t0 t2 (refl_equal T t) (H t2 h d H3)) t1 (lift_inj t t1 h d H4)))) H2)))))))) ts))))) xs). +(* COMMENTS +Initial nodes: 772 +END *) theorem lift_free: \forall (t: T).(\forall (h: nat).(\forall (k: nat).(\forall (d: @@ -484,6 +505,9 @@ k e (plus d h) H1) (plus (s k d) h) (s_plus k d h)) (s_le k d e H2))) (lift (THead k (lift h d t0) (lift h (s k d) t1))) (lift_head k (lift h d t0) (lift h (s k d) t1) k0 e)) (lift h d (THead k t0 t1)) (lift_head k t0 t1 h d))))))))))))) t). +(* COMMENTS +Initial nodes: 1407 +END *) theorem lift_d: \forall (t: T).(\forall (h: nat).(\forall (k: nat).(\forall (d: @@ -562,4 +586,7 @@ d)) (lift k0 e (THead k (lift h d t0) (lift h (s k d) t1))) (lift_head k (lift_head k t0 t1 h d)) (lift h (plus k0 d) (THead k (lift k0 e t0) (lift k0 (s k e) t1))) (lift_head k (lift k0 e t0) (lift k0 (s k e) t1) h (plus k0 d))) (lift k0 e (THead k t0 t1)) (lift_head k t0 t1 k0 e)))))))))))) t). +(* COMMENTS +Initial nodes: 2143 +END *)