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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.
Claim L8: 68498.. 5 (f4b0e.. x0 x1 x2 x3)
Apply unknownprop_0baa02f7150c0866934da98d7084f1221a506b850ca6a82af7a78033da3423bf with x0, x1, x2, x3 leaving 4 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.
Claim L9: 68498.. 6 (binunion (f4b0e.. x0 x1 x2 x3) {(λ x9 . SetAdjoin x9 (Sing 5)) x8|x8 ∈ x4})
Apply unknownprop_ddfc870a0f67dd8bf5406d70b56c890bf0a0c8baf75fc04a131d801e13a59627 with 5, f4b0e.. x0 x1 x2 x3, x4 leaving 4 subgoals.
The subproof is completed by applying nat_5.
The subproof is completed by applying In_1_5.
The subproof is completed by applying L8.
The subproof is completed by applying H4.
Claim L10: 68498.. 7 (binunion (binunion (f4b0e.. x0 x1 x2 x3) {(λ x9 . SetAdjoin x9 (Sing 5)) x8|x8 ∈ x4}) {(λ x9 . SetAdjoin x9 (Sing 6)) x8|x8 ∈ x5})
Apply unknownprop_ddfc870a0f67dd8bf5406d70b56c890bf0a0c8baf75fc04a131d801e13a59627 with 6, binunion (f4b0e.. x0 x1 x2 x3) {(λ x9 . SetAdjoin x9 (Sing 5)) x8|x8 ∈ x4}, x5 leaving 4 subgoals.
The subproof is completed by applying nat_6.
The subproof is completed by applying In_1_6.
The subproof is completed by applying L9.
The subproof is completed by applying H5.
Claim L11: 68498.. 8 (binunion (binunion (binunion (f4b0e.. x0 x1 x2 x3) {(λ x9 . SetAdjoin x9 (Sing 5)) x8|x8 ∈ x4}) {(λ x9 . SetAdjoin x9 (Sing 6)) x8|x8 ∈ x5}) {(λ x9 . SetAdjoin x9 (Sing 7)) x8|x8 ∈ x6})
Apply unknownprop_ddfc870a0f67dd8bf5406d70b56c890bf0a0c8baf75fc04a131d801e13a59627 with 7, binunion (binunion (f4b0e.. x0 x1 x2 x3) {(λ x9 . SetAdjoin x9 (Sing 5)) x8|x8 ∈ x4}) {(λ x9 . SetAdjoin x9 (Sing 6)) x8|x8 ∈ x5}, x6 leaving 4 subgoals.
The subproof is completed by applying nat_7.
The subproof is completed by applying In_1_7.
The subproof is completed by applying L10.
The subproof is completed by applying H6.
Apply unknownprop_ddfc870a0f67dd8bf5406d70b56c890bf0a0c8baf75fc04a131d801e13a59627 with 8, binunion (binunion (binunion (f4b0e.. x0 x1 x2 x3) {(λ x9 . SetAdjoin x9 (Sing 5)) x8|x8 ∈ x4}) {(λ x9 . SetAdjoin x9 (Sing 6)) x8|x8 ∈ x5}) {(λ x9 . SetAdjoin x9 (Sing 7)) x8|x8 ∈ x6}, x7 leaving 4 subgoals.
The subproof is completed by applying nat_8.
The subproof is completed by applying In_1_8.
The subproof is completed by applying L11.
The subproof is completed by applying H7.
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