Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply add_SNoCutP_lem with
x0,
x1,
x2,
x3,
x4,
x5,
add_SNo x4 x5 = SNoCut (binunion {add_SNo x6 x5|x6 ∈ x0} {add_SNo x4 x6|x6 ∈ x2}) (binunion {add_SNo x6 x5|x6 ∈ x1} {add_SNo x4 x6|x6 ∈ x3}) leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H5.