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.
Let x7 of type ι be given.
Assume H6: x7 ∈ x0.
Assume H7: x1 = x2 ⟶ ∀ x8 : ο . x8.
Assume H8: x1 = x3 ⟶ ∀ x8 : ο . x8.
Assume H9: x2 = x3 ⟶ ∀ x8 : ο . x8.
Assume H10: x1 = x4 ⟶ ∀ x8 : ο . x8.
Assume H11: x2 = x4 ⟶ ∀ x8 : ο . x8.
Assume H12: x3 = x4 ⟶ ∀ x8 : ο . x8.
Assume H13: x1 = x5 ⟶ ∀ x8 : ο . x8.
Assume H14: x2 = x5 ⟶ ∀ x8 : ο . x8.
Assume H15: x3 = x5 ⟶ ∀ x8 : ο . x8.
Assume H16: x4 = x5 ⟶ ∀ x8 : ο . x8.
Assume H17: x1 = x6 ⟶ ∀ x8 : ο . x8.
Assume H18: x2 = x6 ⟶ ∀ x8 : ο . x8.
Assume H19: x3 = x6 ⟶ ∀ x8 : ο . x8.
Assume H20: x4 = x6 ⟶ ∀ x8 : ο . x8.
Assume H21: x5 = x6 ⟶ ∀ x8 : ο . x8.
Assume H22: x1 = x7 ⟶ ∀ x8 : ο . x8.
Assume H23: x2 = x7 ⟶ ∀ x8 : ο . x8.
Assume H24: x3 = x7 ⟶ ∀ x8 : ο . x8.
Assume H25: x4 = x7 ⟶ ∀ x8 : ο . x8.
Assume H26: x5 = x7 ⟶ ∀ x8 : ο . x8.
Assume H27: x6 = x7 ⟶ ∀ x8 : ο . x8.
Apply setminusI with
x0,
Sing x7,
x3 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H30:
x3 ∈ Sing x7.
Apply H24.
Apply SingE with
x7,
x3.
The subproof is completed by applying H30.
Apply setminusI with
x0,
Sing x7,
x4 leaving 2 subgoals.
The subproof is completed by applying H3.
Assume H31:
x4 ∈ Sing x7.
Apply H25.
Apply SingE with
x7,
x4.
The subproof is completed by applying H31.
Apply setminusI with
x0,
Sing x7,
x5 leaving 2 subgoals.
The subproof is completed by applying H4.
Assume H32:
x5 ∈ Sing x7.
Apply H26.
Apply SingE with
x7,
x5.
The subproof is completed by applying H32.
Apply setminusI with
x0,
Sing x7,
x6 leaving 2 subgoals.
The subproof is completed by applying H5.
Assume H33:
x6 ∈ Sing x7.
Apply H27.
Apply SingE with
x7,
x6.
The subproof is completed by applying H33.
Apply setminus_nIn_I2 with
x0,
Sing x7,
x7.
The subproof is completed by applying SingI with x7.
Apply unknownprop_177f188aeb617b414c6fa5900e9327cfbb8730aaf66e8869e02cfe5ca96c547d with
setminus x0 (Sing x7),
x1,
x2,
x3,
x4,
x5,
x6 leaving 21 subgoals.
The subproof is completed by applying L28.
The subproof is completed by applying L29.
The subproof is completed by applying L30.
The subproof is completed by applying L31.
The subproof is completed by applying L32.
The subproof is completed by applying L33.
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.
The subproof is completed by applying H16.
The subproof is completed by applying H17.
The subproof is completed by applying H18.
The subproof is completed by applying H19.
The subproof is completed by applying H20.
The subproof is completed by applying H21.
Apply unknownprop_20fce6fc7f2e036c1229cbf996632439eddb19cfae541105a83e5be9c65bc111 with
x0,
x7,
λ x8 x9 . atleastp u7 x9 leaving 2 subgoals.
The subproof is completed by applying H6.
Apply unknownprop_11c6158bd93dbd27daaa9a84a43404be6ccbf75f900b1e28dfa453e64ea6c96b with
u6,
setminus x0 (Sing x7),
x7 leaving 2 subgoals.
The subproof is completed by applying L34.
The subproof is completed by applying L35.