theorem ntrack_weak: \forall R,p,P,Q,S,i.
NTrack P p S \to Insert R i P Q \to
\exists q. NTrack Q q S.
intros 2; elim p; clear p;
[ lapply linear ntrack_inv_lref to H as H0; decompose;
lapply linear insert_trans to H, H1; decompose; autobatch
theorem ntrack_weak: \forall R,p,P,Q,S,i.
NTrack P p S \to Insert R i P Q \to
\exists q. NTrack Q q S.
intros 2; elim p; clear p;
[ lapply linear ntrack_inv_lref to H as H0; decompose;
lapply linear insert_trans to H, H1; decompose; autobatch
- | lapply linear ntrack_inv_parx to H; subst; autobatch
- | lapply linear ntrack_inv_impw to H1; decompose; subst;
+ | lapply linear ntrack_inv_parx to H; destruct; autobatch
+ | lapply linear ntrack_inv_impw to H1; decompose; destruct;
lapply insert_conf to H4, H6; clear H6; decompose;
lapply H to H9, H4; clear H H9; lapply linear H1 to H8, H4;
lapply linear H2 to H7, H6; decompose; autobatch width = 4
lapply insert_conf to H4, H6; clear H6; decompose;
lapply H to H9, H4; clear H H9; lapply linear H1 to H8, H4;
lapply linear H2 to H7, H6; decompose; autobatch width = 4
- lapply linear insert_conf_rev_full to H1,H2; decompose; subst; autobatch
- | lapply linear ntrack_inv_parx to H1; subst; autobatch
- | lapply linear ntrack_inv_impw to H2; decompose; subst;
+ lapply linear insert_conf_rev_full to H1,H2; decompose; destruct; autobatch
+ | lapply linear ntrack_inv_parx to H1; destruct; autobatch
+ | lapply linear ntrack_inv_impw to H2; decompose; destruct;
lapply insert_trans to H5, H7; clear H7; decompose;
lapply ntrack_weak to H3, H6; decompose;
lapply H to H3, H10, H5; clear H H10; lapply linear H1 to H3, H9, H5;
lapply insert_trans to H5, H7; clear H7; decompose;
lapply ntrack_weak to H3, H6; decompose;
lapply H to H3, H10, H5; clear H H10; lapply linear H1 to H3, H9, H5;
theorem ntrack_track: \forall R,p,P. NTrack P p R \to Track P p R.
intros; elim H names 0; clear H P p R; intros; autobatch width = 4.
qed.
theorem ntrack_track: \forall R,p,P. NTrack P p R \to Track P p R.
intros; elim H names 0; clear H P p R; intros; autobatch width = 4.
qed.