Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply binunionE with
x0,
x1,
x2,
x2 ∈ binunion x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1: x2 ∈ x0.
Apply binunionI2 with
x1,
x0,
x2.
The subproof is completed by applying H1.
Assume H1: x2 ∈ x1.
Apply binunionI1 with
x1,
x0,
x2.
The subproof is completed by applying H1.