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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.
Let x8 of type ι be given.
Let x9 of type ι be given.
Let x10 of type ι be given.
Let x11 of type ι be given.
Let x12 of type ι be given.
Let x13 of type ι be given.
Let x14 of type ι be given.
Let x15 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: SNo x8.
Assume H9: SNo x9.
Assume H10: SNo x10.
Assume H11: SNo x11.
Assume H12: SNo x12.
Assume H13: SNo x13.
Assume H14: SNo x14.
Assume H15: SNo x15.
Assume H16: bbc71.. x0 x1 x2 x3 x4 x5 x6 x7 = bbc71.. x8 x9 x10 x11 x12 x13 x14 x15.
Claim L17: ...
...
Claim L18: ...
...
Claim L19: ...
...
Claim L20: ...
...
Claim L21: ...
...
Claim L22: ...
...
Claim L23: ...
...
Claim L24: ...
...
Claim L25: binunion (binunion (binunion (f4b0e.. x0 x1 x2 x3) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x4}) ...) ... = ...
...
Claim L26: binunion (binunion (f4b0e.. x0 x1 x2 x3) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x4}) {(λ x17 . SetAdjoin x17 (Sing 6)) x16|x16 ∈ x5} = binunion (binunion (f4b0e.. x8 x9 x10 x11) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x12}) {(λ x17 . SetAdjoin x17 (Sing 6)) x16|x16 ∈ x13}
Apply unknownprop_51bcfb81b3dbbea1e1fae277f714ba4cf628952e82df65fecaaeb1c81602a38b with 7, binunion (binunion (f4b0e.. x0 x1 x2 x3) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x4}) {(λ x17 . SetAdjoin x17 (Sing 6)) x16|x16 ∈ x5}, binunion (binunion (f4b0e.. x8 x9 x10 x11) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x12}) {(λ x17 . SetAdjoin x17 (Sing 6)) x16|x16 ∈ x13}, x6, x14 leaving 5 subgoals.
The subproof is completed by applying nat_7.
The subproof is completed by applying In_1_7.
The subproof is completed by applying L19.
The subproof is completed by applying L23.
The subproof is completed by applying L25.
Claim L27: binunion (f4b0e.. x0 x1 x2 x3) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x4} = binunion (f4b0e.. x8 x9 x10 x11) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x12}
Apply unknownprop_51bcfb81b3dbbea1e1fae277f714ba4cf628952e82df65fecaaeb1c81602a38b with 6, binunion (f4b0e.. x0 x1 x2 x3) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x4}, binunion (f4b0e.. x8 x9 x10 x11) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x12}, x5, x13 leaving 5 subgoals.
The subproof is completed by applying nat_6.
The subproof is completed by applying In_1_6.
The subproof is completed by applying L18.
The subproof is completed by applying L22.
The subproof is completed by applying L26.
Apply unknownprop_2813bbc264ba76c59b7f17aa546b4f6f8aeefd89625c13ba0e93156d0c5da027 with 5, f4b0e.. x0 x1 x2 x3, f4b0e.. x8 x9 x10 x11, x4, x12 leaving 7 subgoals.
The subproof is completed by applying nat_5.
The subproof is completed by applying In_1_5.
The subproof is completed by applying L17.
The subproof is completed by applying L21.
The subproof is completed by applying H4.
The subproof is completed by applying H12.
The subproof is completed by applying L27.
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