Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: x1 ∈ x0.
Let x2 of type ι be given.
Assume H1: x2 ∈ x0.
Let x3 of type ι be given.
Assume H2: x3 ∈ x0.
Let x4 of type ι be given.
Assume H3: x4 ∈ x0.
Let x5 of type ι be given.
Assume H4: x5 ∈ x0.
Let x6 of type ι be given.
Assume H5: x6 ∈ x0.
Assume H6: x1 = x2 ⟶ ∀ x7 : ο . x7.
Assume H7: x1 = x3 ⟶ ∀ x7 : ο . x7.
Assume H8: x2 = x3 ⟶ ∀ x7 : ο . x7.
Assume H9: x1 = x4 ⟶ ∀ x7 : ο . x7.
Assume H10: x2 = x4 ⟶ ∀ x7 : ο . x7.
Assume H11: x3 = x4 ⟶ ∀ x7 : ο . x7.
Assume H12: x1 = x5 ⟶ ∀ x7 : ο . x7.
Assume H13: x2 = x5 ⟶ ∀ x7 : ο . x7.
Assume H14: x3 = x5 ⟶ ∀ x7 : ο . x7.
Assume H15: x4 = x5 ⟶ ∀ x7 : ο . x7.
Assume H16: x1 = x6 ⟶ ∀ x7 : ο . x7.
Assume H17: x2 = x6 ⟶ ∀ x7 : ο . x7.
Assume H18: x3 = x6 ⟶ ∀ x7 : ο . x7.
Assume H19: x4 = x6 ⟶ ∀ x7 : ο . x7.
Assume H20: x5 = x6 ⟶ ∀ x7 : ο . x7.
Apply setminusI with
x0,
Sing x6,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H21:
x1 ∈ Sing x6.
Apply H16.
Apply SingE with
x6,
x1.
The subproof is completed by applying H21.
Apply setminusI with
x0,
Sing x6,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H22:
x2 ∈ Sing x6.
Apply H17.
Apply SingE with
x6,
x2.
The subproof is completed by applying H22.
Apply setminusI with
x0,
Sing x6,
x3 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H23:
x3 ∈ Sing x6.
Apply H18.
Apply SingE with
x6,
x3.
The subproof is completed by applying H23.
Apply setminusI with
x0,
Sing x6,
x4 leaving 2 subgoals.
The subproof is completed by applying H3.
Assume H24:
x4 ∈ Sing x6.
Apply H19.
Apply SingE with
x6,
x4.
The subproof is completed by applying H24.
Apply setminusI with
x0,
Sing x6,
x5 leaving 2 subgoals.
The subproof is completed by applying H4.
Assume H25:
x5 ∈ Sing x6.
Apply H20.
Apply SingE with
x6,
x5.
The subproof is completed by applying H25.
Apply setminus_nIn_I2 with
x0,
Sing x6,
x6.
The subproof is completed by applying SingI with x6.
Apply unknownprop_7e1bdc2c8a21232f1137435691870e9adbcd063b926204c5c33f7957e9bb1899 with
setminus x0 (Sing x6),
x1,
x2,
x3,
x4,
x5 leaving 15 subgoals.
The subproof is completed by applying L21.
The subproof is completed by applying L22.
The subproof is completed by applying L23.
The subproof is completed by applying L24.
The subproof is completed by applying L25.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
The subproof is completed by applying H10.
The subproof is completed by applying H11.
The subproof is completed by applying H12.
The subproof is completed by applying H13.
The subproof is completed by applying H14.
The subproof is completed by applying H15.
Apply unknownprop_20fce6fc7f2e036c1229cbf996632439eddb19cfae541105a83e5be9c65bc111 with
x0,
x6,
λ x7 x8 . atleastp u6 x8 leaving 2 subgoals.
The subproof is completed by applying H5.
Apply unknownprop_11c6158bd93dbd27daaa9a84a43404be6ccbf75f900b1e28dfa453e64ea6c96b with
u5,
setminus x0 (Sing x6),
x6 leaving 2 subgoals.
The subproof is completed by applying L26.
The subproof is completed by applying L27.