Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply UnionE_impred with
prim2 x0 x1,
x2,
or (prim1 x2 x0) (prim1 x2 x1) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ι be given.
Apply unknownprop_44132e34b8fcc92e54ff875d0e8f6137eeea7d41bb9d4b117dbbbb4d2f239782 with
x3,
x0,
x1,
or (prim1 x2 x0) (prim1 x2 x1) leaving 3 subgoals.
The subproof is completed by applying H2.
Assume H3: x3 = x0.
Apply orIL with
prim1 x2 x0,
prim1 x2 x1.
Apply H3 with
λ x4 x5 . prim1 x2 x4.
The subproof is completed by applying H1.
Assume H3: x3 = x1.
Apply orIR with
prim1 x2 x0,
prim1 x2 x1.
Apply H3 with
λ x4 x5 . prim1 x2 x4.
The subproof is completed by applying H1.