Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: x0 ⊆ x1.
Let x2 of type ι be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι be given.
Assume H2: x4 ⊆ x2.
Apply H1 with
x4 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply atleastp_tra with
x0,
x1,
x4 leaving 2 subgoals.
Apply Subq_atleastp with
x0,
x1.
The subproof is completed by applying H0.
The subproof is completed by applying H3.