Search for blocks/addresses/...

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: 68498.. 6 (binunion (f4b0e.. x8 x9 x10 x11) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x12})
Apply unknownprop_ddfc870a0f67dd8bf5406d70b56c890bf0a0c8baf75fc04a131d801e13a59627 with 5, f4b0e.. ... ... ... ..., ... leaving 4 subgoals.
...
...
...
...
Claim L23: 68498.. 7 (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_ddfc870a0f67dd8bf5406d70b56c890bf0a0c8baf75fc04a131d801e13a59627 with 6, binunion (f4b0e.. x8 x9 x10 x11) {(λ x17 . SetAdjoin x17 (Sing 5)) x16|x16 ∈ x12}, x13 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 L22.
The subproof is completed by applying H13.
Claim L24: 68498.. 8 (binunion (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}) {(λ x17 . SetAdjoin x17 (Sing 7)) x16|x16 ∈ x14})
Apply unknownprop_ddfc870a0f67dd8bf5406d70b56c890bf0a0c8baf75fc04a131d801e13a59627 with 7, 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}, x14 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 L23.
The subproof is completed by applying H14.
Apply unknownprop_2813bbc264ba76c59b7f17aa546b4f6f8aeefd89625c13ba0e93156d0c5da027 with 8, binunion (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}) {(λ x17 . SetAdjoin x17 (Sing 7)) x16|x16 ∈ x6}, binunion (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}) {(λ x17 . SetAdjoin x17 (Sing 7)) x16|x16 ∈ x14}, x7, x15 leaving 7 subgoals.
The subproof is completed by applying nat_8.
The subproof is completed by applying In_1_8.
The subproof is completed by applying L20.
The subproof is completed by applying L24.
The subproof is completed by applying H7.
The subproof is completed by applying H15.
The subproof is completed by applying H16.
■