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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 x4.
Assume H4: SNo x5.
Assume H5: SNo x6.
Assume H6: 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 L7: ...
...
Claim L8: ...
...
Claim L9: 68498.. 3 (binunion x4 {(λ x9 . SetAdjoin x9 (Sing 2)) x8|x8 ∈ x5})
Apply unknownprop_d70cc86669636f09f3d7916eef547e3c121ef7467f1e4baa7bd1bb2d082b0fbe with x4, x5 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L10: 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 L9.
The subproof is completed by applying H5.
Claim L11: 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 L8.
The subproof is completed by applying L10.
The subproof is completed by applying H6.
Claim L12: 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 L7.
The subproof is completed by applying L9.
The subproof is completed by applying L11.
Apply unknownprop_51bcfb81b3dbbea1e1fae277f714ba4cf628952e82df65fecaaeb1c81602a38b with 2, x0, x4, x1, x5 leaving 5 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 H3.
The subproof is completed by applying L12.
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