- (* a "ClosedND" is a proof with no open hypotheses and no multi-conclusion rules *)
- Inductive ClosedND : Tree ??Judgment -> Type :=
- | cnd_weak : ClosedND []
- | cnd_rule : forall h c , ClosedND h -> Rule h c -> ClosedND c
- | cnd_branch : forall c1 c2, ClosedND c1 -> ClosedND c2 -> ClosedND (c1,,c2)
+ (* a "ClosedSIND" is a proof with no open hypotheses and no multi-conclusion rules *)
+ Inductive ClosedSIND : Tree ??Judgment -> Type :=
+ | cnd_weak : ClosedSIND []
+ | cnd_rule : forall h c , ClosedSIND h -> Rule h c -> ClosedSIND c
+ | cnd_branch : forall c1 c2, ClosedSIND c1 -> ClosedSIND c2 -> ClosedSIND (c1,,c2)