Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι be given.
Assume H0: ∀ x3 . x3 ∈ x0 ⟶ x1 x3 = x2 x3.
Apply set_ext with
famunion x0 x1,
famunion x0 x2 leaving 2 subgoals.
Apply famunion_Subq with
x0,
x1,
x2.
Let x3 of type ι be given.
Assume H1: x3 ∈ x0.
Apply H0 with
x3,
λ x4 x5 . x5 ⊆ x2 x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying Subq_ref with x2 x3.
Apply famunion_Subq with
x0,
x2,
x1.
Let x3 of type ι be given.
Assume H1: x3 ∈ x0.
Apply H0 with
x3,
λ x4 x5 . x2 x3 ⊆ x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying Subq_ref with x2 x3.