Let x0 of type ι be given.
Let x1 of type ι be given.
Apply prop_ext_2 with
Subq x0 x1,
binintersect x0 x1 = x0 leaving 2 subgoals.
Apply unknownprop_a23ec6a55ac212526d74cbf0d04096929ad453b0eb0f8023e32b8a33930d39fb with
binintersect x0 x1,
x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_e0d452e0e0459ccd22d0a0ca66d8c6b520f69a835c0ebd50bbdd40077efd4a68 with x0, x1.
Apply unknownprop_b493a75fcec57593a6576a7c6d850d3d24c9ed1931af4734bd2773dfce586a4d with
x0,
x1,
x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_d889823a5c975ad2d68f484964233a1e69e7d67f0888aa5b83d962eeca107acd with x0.
The subproof is completed by applying H0.
Apply H0 with
λ x2 x3 . Subq x2 x1.
The subproof is completed by applying unknownprop_43a7b6a7250420244ab59ee561112cfc53c614b669837fc84c919b0df2ef6e0a with x0, x1.