identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.


%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (_ : left (? P) -> right (? P)).

%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

%worlds () (identity _ _).
%total A (identity A _).

###

identity.elf:7.8-7.9 Error:
Coverage error --- missing cases:
{A1:prop} {A2:prop} {X1:left (A1 => A2) -> right (A1 => A2)}
   |- identity (A1 => A2) ([x:left (A1 => A2)] X1 x),
{A1:prop} {A2:prop} {X1:left (A1 /\ A2) -> right (A1 /\ A2)}
   |- identity (A1 /\ A2) ([x:left (A1 /\ A2)] X1 x).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

id/\ : identity (A /\ B)
                (_ : left (A /\ B) -> right (A /\ B)).

%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

id/\ : identity (A /\ B)
                ([u:left (A /\ B)]
                 _ : right (A /\ B)).

%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

id/\ : identity (A /\ B)
                ([u:left (A /\ B)]
                 /\R (_ : right A)
                     (_ : right B)).

%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

id/\ : identity (A /\ B)
                ([u:left (A /\ B)]
                 /\R (/\L1 (_ : left A -> right A)
                           (_ : left (A /\ B)))
                     (_ : right B)).

%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

id/\ : identity (A /\ B)
                ([u:left (A /\ B)]
                 /\R (/\L1 (_ : left A -> right A)
                           (u : left (A /\ B)))
                     (_ : right B)).

%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

id/\ : identity (A /\ B)
                ([u:left (A /\ B)]
                 /\R (/\L1 (_ : left A -> right A)
                           (u : left (A /\ B)))
                     (_ : right B))
        <- identity A (IdA : left A -> right A).

%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

id/\ : identity (A /\ B)
                ([u:left (A /\ B)]
                 /\R (/\L1 (IdA : left A -> right A)
                           (u : left (A /\ B)))
                     (_ : right B))
        <- identity A (IdA : left A -> right A).

%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

id/\ : identity (A /\ B)
                ([u:left (A /\ B)]
                 /\R (/\L1 IdA u)
                     (_ : right B))
        <- identity A (IdA : left A -> right A).

%worlds () (identity _ _).
%total A (identity A _).

%%%

identity : {A:prop} (left A -> right A) -> type.
%mode identity +A -D.

id?  : identity (? P) (init : left (? P) -> right (? P)).

id/\ : identity (A /\ B)
                ([u:left (A /\ B)]
                 /\R (/\L1 IdA u)
                     (/\L2 IdB u))
        <- identity A (IdA : left A -> right A)
        <- identity B (IdB : left B -> right B).

%worlds () (identity _ _).
%total A (identity A _).

###

identity.elf:14.8-14.9 Error:
Coverage error --- missing cases:
{A1:prop} {A2:prop} {X1:left (A1 => A2) -> right (A1 => A2)}
   |- identity (A1 => A2) ([x:left (A1 => A2)] X1 x).