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.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_d70cc86669636f09f3d7916eef547e3c121ef7467f1e4baa7bd1bb2d082b0fbe with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_ddfc870a0f67dd8bf5406d70b56c890bf0a0c8baf75fc04a131d801e13a59627 with
3,
binunion x0 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x1},
x2 leaving 4 subgoals.
The subproof is completed by applying nat_3.
The subproof is completed by applying In_1_3.
The subproof is completed by applying L9.
The subproof is completed by applying H2.
Apply unknownprop_d70cc86669636f09f3d7916eef547e3c121ef7467f1e4baa7bd1bb2d082b0fbe with
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Apply unknownprop_ddfc870a0f67dd8bf5406d70b56c890bf0a0c8baf75fc04a131d801e13a59627 with
3,
binunion x4 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x5},
x6 leaving 4 subgoals.
The subproof is completed by applying nat_3.
The subproof is completed by applying In_1_3.
The subproof is completed by applying L11.
The subproof is completed by applying H6.
Apply unknownprop_2813bbc264ba76c59b7f17aa546b4f6f8aeefd89625c13ba0e93156d0c5da027 with
4,
binunion (binunion x0 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x1}) {(λ x9 . SetAdjoin x9 (Sing 3)) x8|x8 ∈ x2},
binunion (binunion x4 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x5}) {(λ x9 . SetAdjoin x9 (Sing 3)) x8|x8 ∈ x6},
x3,
x7 leaving 7 subgoals.
The subproof is completed by applying nat_4.
The subproof is completed by applying In_1_4.
The subproof is completed by applying L10.
The subproof is completed by applying L12.
The subproof is completed by applying H3.
The subproof is completed by applying H7.
The subproof is completed by applying H8.