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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιιο be given.
Assume H0: ∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2.
Assume H1: 4402e.. x0 x1.
Let x2 of type ι be given.
Assume H2: x2x0.
Let x3 of type ι be given.
Assume H3: x3x0.
Let x4 of type ι be given.
Assume H4: x4x0.
Assume H5: x2 = x3∀ x5 : ο . x5.
Assume H6: x2 = x4∀ x5 : ο . x5.
Assume H7: x3 = x4∀ x5 : ο . x5.
Assume H8: x1 x2 x3.
Assume H9: x1 x2 x4.
Assume H10: x1 x3 x4.
Apply H1 with SetAdjoin (UPair x2 x3) x4 leaving 3 subgoals.
Apply unknownprop_434e2e2330a02d70f83efc2b51c595946aeb4462c38cf32d55a1757fe463ba11 with x2, x3, x4, λ x5 . x5x0 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply equip_atleastp with u3, SetAdjoin (UPair x2 x3) x4.
Apply unknownprop_637144c754e35176e5f73e9789b35a2d801de40f26463f5ae01a3b9c5aad6047 with x2, x3, x4 leaving 3 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
Apply unknownprop_434e2e2330a02d70f83efc2b51c595946aeb4462c38cf32d55a1757fe463ba11 with x2, x3, x4, λ x5 . ∀ x6 . x6SetAdjoin (UPair x2 x3) x4(x5 = x6∀ x7 : ο . x7)x1 x5 x6 leaving 3 subgoals.
Apply unknownprop_434e2e2330a02d70f83efc2b51c595946aeb4462c38cf32d55a1757fe463ba11 with x2, x3, x4, λ x5 . (x2 = x5∀ x6 : ο . x6)x1 x2 x5 leaving 3 subgoals.
Assume H11: x2 = x2∀ x5 : ο . x5.
Apply FalseE with x1 x2 x2.
Apply H11.
Let x5 of type ιιο be given.
Assume H12: x5 x2 x2.
The subproof is completed by applying H12.
Assume H11: x2 = x3∀ x5 : ο . x5.
The subproof is completed by applying H8.
Assume H11: x2 = x4∀ x5 : ο . x5.
The subproof is completed by applying H9.
Apply unknownprop_434e2e2330a02d70f83efc2b51c595946aeb4462c38cf32d55a1757fe463ba11 with x2, x3, x4, λ x5 . (x3 = x5∀ x6 : ο . x6)x1 x3 x5 leaving 3 subgoals.
Assume H11: x3 = x2∀ x5 : ο . x5.
Apply H0 with x2, x3 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H8.
Assume H11: x3 = x3∀ x5 : ο . x5.
Apply FalseE with x1 x3 x3.
Apply H11.
Let x5 of type ιιο be given.
Assume H12: x5 x3 x3.
The subproof is completed by applying H12.
Assume H11: x3 = x4∀ x5 : ο . x5.
The subproof is completed by applying H10.
Apply unknownprop_434e2e2330a02d70f83efc2b51c595946aeb4462c38cf32d55a1757fe463ba11 with x2, x3, x4, λ x5 . (x4 = x5∀ x6 : ο . x6)x1 x4 x5 leaving 3 subgoals.
Assume H11: x4 = x2∀ x5 : ο . x5.
Apply H0 with x2, x4 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
The subproof is completed by applying H9.
Assume H11: x4 = x3∀ x5 : ο . x5.
Apply H0 with x3, x4 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H10.
Assume H11: x4 = x4∀ x5 : ο . x5.
Apply FalseE with x1 x4 x4.
Apply H11.
Let x5 of type ιιο be given.
Assume H12: x5 x4 x4.
The subproof is completed by applying H12.