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Proofgold Proof

pf
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.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNo x3.
Assume H4: SNo x4.
Assume H5: SNo x5.
Assume H6: SNo x6.
Assume H7: SNo x7.
Assume H8: binunion (binunion (binunion x0 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x1}) {(λ x9 . SetAdjoin x9 (Sing 3)) x8|x8 ∈ x2}) {(λ x9 . SetAdjoin x9 (Sing 4)) x8|x8 ∈ x3} = binunion (binunion (binunion x4 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x5}) {(λ x9 . SetAdjoin x9 (Sing 3)) x8|x8 ∈ x6}) {(λ x9 . SetAdjoin x9 (Sing 4)) x8|x8 ∈ x7}.
Claim L9: ...
...
Claim L10: ...
...
Claim L11: 68498.. 3 (binunion x4 {(λ x9 . SetAdjoin x9 (Sing 2)) ...|x8 ∈ x5})
...
Claim L12: 68498.. 4 (binunion (binunion x4 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x5}) {(λ x9 . SetAdjoin x9 (Sing 3)) x8|x8 ∈ x6})
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.
Claim L13: 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}
Apply unknownprop_51bcfb81b3dbbea1e1fae277f714ba4cf628952e82df65fecaaeb1c81602a38b 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 5 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 H8.
Claim L14: binunion x0 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x1} = binunion x4 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x5}
Apply unknownprop_51bcfb81b3dbbea1e1fae277f714ba4cf628952e82df65fecaaeb1c81602a38b with 3, binunion x0 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x1}, binunion x4 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x5}, x2, x6 leaving 5 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 L11.
The subproof is completed by applying L13.
Apply unknownprop_2813bbc264ba76c59b7f17aa546b4f6f8aeefd89625c13ba0e93156d0c5da027 with 2, x0, x4, x1, x5 leaving 7 subgoals.
The subproof is completed by applying nat_2.
The subproof is completed by applying In_1_2.
Apply unknownprop_a4edcbab661199d6911d1441c90756c844d60baa5bb17d517bccec0c64f7803b with x0, 2.
The subproof is completed by applying H0.
Apply unknownprop_a4edcbab661199d6911d1441c90756c844d60baa5bb17d517bccec0c64f7803b with x4, 2.
The subproof is completed by applying H4.
The subproof is completed by applying H1.
The subproof is completed by applying H5.
The subproof is completed by applying L14.
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