Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Assume H0: x0 ⊆ x1.
Assume H1: ∀ x3 . x3 ⊆ x1 ⟶ x2 x3.
Let x3 of type ι be given.
Assume H2: x3 ⊆ x0.
Apply H1 with
x3.
Apply Subq_tra with
x3,
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H0.