(* Specifications: *)
Theorem Lem20 : forall d : D, seq (ia frame c6 (tuple e0)) (Y1 d) = enc H (mer (seq (ia frame s6 (tuple e0)) (L i)) (mer (seq (Rn e0) (R i)) (mer (K i) (seq (Tn_d d e1) (S i))))) :>proc.
Theorem Lem21 : forall d : D, seq (ia frame c6 sce) (Y1 d) = enc H (mer (seq (ia frame s6 sce) (L i)) (mer (seq (Rn e0) (R i)) (mer (K i) (seq (Tn_d d e1) (S i))))).
Theorem Lem10 : forall d : D, seq (ia frame c6 (tuple e1)) (X1 d) = enc H (mer (seq (ia frame s6 (tuple e1)) (L i)) (mer (R i) (mer (K i) (seq (Tn_d d e0) (seq (Sn e1) (S i)))))).
Theorem Lem11 : forall d : D, seq (ia frame c6 sce) (X1 d) = enc H (mer (seq (ia frame s6 sce) (L i)) (mer (R i) (mer (K i) (seq (Tn_d d e0) (seq (Sn e1) (S i)))))).
Theorem Lem12 : forall d : D, seq (ia Frame c2 (Tuple e0 d)) (alt (seq (ia one int i) (seq (ia Frame c3 (Tuple e0 d)) (seq (ia D s4 d) (X2 d)))) (seq (ia one int i) (seq (ia Frame c3 lce) (seq (ia frame c5 (tuple e1)) (seq (alt (seq (ia one int i) (ia frame c6 (tuple e1))) (seq (ia one int i) (ia frame c6 sce))) (X1 d)))))) = X1 d.
Theorem Lem13 : forall d : D, seq (ia Frame c2 (Tuple e1 d)) (enc H (mer (seq (Tn_d d e1) (S i)) (mer (seq (alt (seq (ia one int i) (ia Frame s3 (Tuple e1 d))) (seq (ia one int i) (ia Frame s3 lce))) (K i)) (mer (L i) (seq (Rn e0) (R i)))))) = Y1 d.
Theorem Lem14 : forall d : D, alt (seq (ia one int i) (enc H (mer (seq (ia Frame s3 (Tuple e1 d)) (K i)) (mer (seq (Tn_d d e1) (S i)) (mer (L i) (seq (Rn e0) (R i))))))) (seq (ia one int i) (enc H (mer (seq (ia Frame s3 lce) (K i)) (mer (seq (Tn_d d e1) (S i)) (mer (L i) (seq (Rn e0) (R i))))))) = enc H (mer (seq (Tn_d d e1) (S i)) (mer (seq (alt (seq (ia one int i) (ia Frame s3 (Tuple e1 d))) (seq (ia one int i) (ia Frame s3 lce))) (K i)) (mer (L i) (seq (Rn e0) (R i))))).
Theorem Lem15 : forall d : D, seq (ia Frame c3 lce) (enc H (mer (K i) (mer (seq (ia frame s5 (tuple e0)) (seq (Rn e0) (R i))) (mer (seq (Tn_d d e1) (S i)) (L i))))) = enc H (mer (seq (ia Frame s3 lce) (K i)) (mer (seq (Tn_d d e1) (S i)) (mer (L i) (seq (Rn e0) (R i))))).
Theorem Lem16 : forall d : D, seq (ia Frame c3 (Tuple e1 d)) (enc H (mer (K i) (mer (seq (ia D s4 d) (seq (ia frame s5 (tuple e1)) (R i))) (mer (seq (Tn_d d e1) (S i)) (L i))))) = enc H (mer (seq (ia Frame s3 (Tuple e1 d)) (K i)) (mer (seq (Tn_d d e1) (S i)) (mer (L i) (seq (Rn e0) (R i))))).
Theorem Lem17 : forall d : D, seq (ia D s4 d) (Y2 d) = enc H (mer (K i) (mer (seq (ia D s4 d) (seq (ia frame s5 (tuple e1)) (R i))) (mer (seq (Tn_d d e1) (S i)) (L i)))).
Theorem Lem18 : forall d : D, seq (ia frame c5 (tuple e0)) (enc H (mer (seq (Rn e0) (R i)) (mer (alt (seq (ia one int i) (seq (ia frame s6 (tuple e0)) (L i))) (seq (ia one int i) (seq (ia frame s6 sce) (L i)))) (mer (K i) (seq (Tn_d d e1) (S i)))))) = enc H (mer (K i) (mer (seq (ia frame s5 (tuple e0)) (seq (Rn e0) (R i))) (mer (seq (Tn_d d e1) (S i)) (L i)))).
Theorem Lem19 : forall d : D, alt (seq (ia one int i) (enc H (mer (seq (ia frame s6 (tuple e0)) (L i)) (mer (seq (Rn e0) (R i)) (mer (K i) (seq (Tn_d d e1) (S i))))))) (seq (ia one int i) (enc H (mer (seq (ia frame s6 sce) (L i)) (mer (seq (Rn e0) (R i)) (mer (K i) (seq (Tn_d d e1) (S i))))))) = enc H (mer (seq (Rn e0) (R i)) (mer (alt (seq (ia one int i) (seq (ia frame s6 (tuple e0)) (L i))) (seq (ia one int i) (seq (ia frame s6 sce) (L i)))) (mer (K i) (seq (Tn_d d e1) (S i))))).
Theorem Lem1 : D + (fun d : D => seq (ia D r1 d) (X1 d)) = X.
Theorem Lem2 : D + (fun d : D => seq (ia D r1 d) (Y1 d)) = Y.
Theorem Lem3 : forall d : D, seq (ia Frame c2 (Tuple e0 d)) (enc H (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (mer (seq (alt (seq (ia one int i) (ia Frame s3 (Tuple e0 d))) (seq (ia one int i) (ia Frame s3 lce))) (K i)) (mer (L i) (R i))))) = X1 d.
Theorem Lem4 : forall d : D, alt (seq (ia one int i) (enc H (mer (seq (ia Frame s3 (Tuple e0 d)) (K i)) (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (mer (L i) (R i)))))) (seq (ia one int i) (enc H (mer (seq (ia Frame s3 lce) (K i)) (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (mer (L i) (R i)))))) = enc H (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (mer (seq (alt (seq (ia one int i) (ia Frame s3 (Tuple e0 d))) (seq (ia one int i) (ia Frame s3 lce))) (K i)) (mer (L i) (R i)))).
Theorem Lem5 : forall d : D, seq (ia Frame c3 lce) (enc H (mer (K i) (mer (seq (ia frame s5 (tuple e1)) (R i)) (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (L i))))) = enc H (mer (seq (ia Frame s3 lce) (K i)) (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (mer (L i) (R i)))).
Theorem Lem6 : forall d : D, seq (ia Frame c3 (Tuple e0 d)) (enc H (mer (K i) (mer (seq (ia D s4 d) (seq (ia frame s5 (tuple e0)) (seq (Rn e0) (R i)))) (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (L i))))) = enc H (mer (seq (ia Frame s3 (Tuple e0 d)) (K i)) (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (mer (L i) (R i)))).
Theorem Lem7 : forall d : D, seq (ia D s4 d) (X2 d) = enc H (mer (K i) (mer (seq (ia D s4 d) (seq (ia frame s5 (tuple e0)) (seq (Rn e0) (R i)))) (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (L i)))).
Theorem Lem8 : forall d : D, seq (ia frame c5 (tuple e1)) (enc H (mer (R i) (mer (alt (seq (ia one int i) (seq (ia frame s6 (tuple e1)) (L i))) (seq (ia one int i) (seq (ia frame s6 sce) (L i)))) (mer (K i) (seq (Tn_d d e0) (seq (Sn e1) (S i))))))) = enc H (mer (K i) (mer (seq (ia frame s5 (tuple e1)) (R i)) (mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (L i)))).
Theorem Lem9 : forall d : D, alt (seq (ia one int i) (enc H (mer (seq (ia frame s6 (tuple e1)) (L i)) (mer (R i) (mer (K i) (seq (Tn_d d e0) (seq (Sn e1) (S i)))))))) (seq (ia one int i) (enc H (mer (seq (ia frame s6 sce) (L i)) (mer (R i) (mer (K i) (seq (Tn_d d e0) (seq (Sn e1) (S i)))))))) = enc H (mer (R i) (mer (alt (seq (ia one int i) (seq (ia frame s6 (tuple e1)) (L i))) (seq (ia one int i) (seq (ia frame s6 sce) (L i)))) (mer (K i) (seq (Tn_d d e0) (seq (Sn e1) (S i)))))).