End SUBST_SOUND.
Module Subst_Sound (VSD: VERISTAR_DEFS) : SUBST_SOUND with Module VSD := VSD.
Module VSD := VSD.

Lemma subst_space_sound : forall i e a,
space_atom_denote (subst_space i e a) =
match a with
| Next x y => space_atom_denote (Next (subst_expr i e x) (subst_expr i e y))
| Lseg x y => space_atom_denote (Lseg (subst_expr i e x) (subst_expr i e y))
end.