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.
Let x8 of type ι be given.
Assume H7: x8 ∈ x0.
Assume H8: x1 = x2 ⟶ ∀ x9 : ο . x9.
Assume H9: x1 = x3 ⟶ ∀ x9 : ο . x9.
Assume H10: x2 = x3 ⟶ ∀ x9 : ο . x9.
Assume H11: x1 = x4 ⟶ ∀ x9 : ο . x9.
Assume H12: x2 = x4 ⟶ ∀ x9 : ο . x9.
Assume H13: x3 = x4 ⟶ ∀ x9 : ο . x9.
Assume H14: x1 = x5 ⟶ ∀ x9 : ο . x9.
Assume H15: x2 = x5 ⟶ ∀ x9 : ο . x9.
Assume H16: x3 = x5 ⟶ ∀ x9 : ο . x9.
Assume H17: x4 = x5 ⟶ ∀ x9 : ο . x9.
Assume H18: x1 = x6 ⟶ ∀ x9 : ο . x9.
Assume H19: x2 = x6 ⟶ ∀ x9 : ο . x9.
Assume H20: x3 = x6 ⟶ ∀ x9 : ο . x9.
Assume H21: x4 = x6 ⟶ ∀ x9 : ο . x9.
Assume H22: x5 = x6 ⟶ ∀ x9 : ο . x9.
Assume H23: x1 = x7 ⟶ ∀ x9 : ο . x9.
Assume H24: x2 = x7 ⟶ ∀ x9 : ο . x9.
Assume H25: x3 = x7 ⟶ ∀ x9 : ο . x9.
Assume H26: x4 = x7 ⟶ ∀ x9 : ο . x9.
Assume H27: x5 = x7 ⟶ ∀ x9 : ο . x9.
Assume H28: x6 = x7 ⟶ ∀ x9 : ο . x9.
Assume H29: x1 = x8 ⟶ ∀ x9 : ο . x9.
Assume H30: x2 = x8 ⟶ ∀ x9 : ο . x9.
Assume H31: x3 = x8 ⟶ ∀ x9 : ο . x9.
Assume H32: x4 = x8 ⟶ ∀ x9 : ο . x9.
Assume H33: x5 = x8 ⟶ ∀ x9 : ο . x9.
Assume H34: x6 = x8 ⟶ ∀ x9 : ο . x9.
Assume H35: x7 = x8 ⟶ ∀ x9 : ο . x9.
Apply setminusI with
x0,
Sing x8,
x6 leaving 2 subgoals.
The subproof is completed by applying H5.
Assume H41:
x6 ∈ Sing x8.
Apply setminusI with
x0,
Sing x8,
x7 leaving 2 subgoals.
The subproof is completed by applying H6.
Assume H42:
x7 ∈ Sing x8.
Apply H35.
Apply SingE with
x8,
x7.
The subproof is completed by applying H42.
Apply setminus_nIn_I2 with
x0,
Sing x8,
x8.
The subproof is completed by applying SingI with x8.
Apply unknownprop_b4405784b5d39999255fee88ce50830138750d1243b8cc1c27f62d3f9efc8a97 with
setminus x0 (Sing x8),
x1,
x2,
x3,
x4,
x5,
x6,
x7 leaving 28 subgoals.
The subproof is completed by applying L36.
The subproof is completed by applying L37.
The subproof is completed by applying L38.
The subproof is completed by applying L39.
The subproof is completed by applying L40.
The subproof is completed by applying L41.
The subproof is completed by applying L42.
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.
The subproof is completed by applying H22.
The subproof is completed by applying H23.
The subproof is completed by applying H24.
The subproof is completed by applying H25.
The subproof is completed by applying H26.
The subproof is completed by applying H27.
The subproof is completed by applying H28.
Apply unknownprop_20fce6fc7f2e036c1229cbf996632439eddb19cfae541105a83e5be9c65bc111 with
x0,
x8,
λ x9 x10 . atleastp u8 x10 leaving 2 subgoals.
The subproof is completed by applying H7.
Apply unknownprop_11c6158bd93dbd27daaa9a84a43404be6ccbf75f900b1e28dfa453e64ea6c96b with
u7,
setminus x0 (Sing x8),
x8 leaving 2 subgoals.
The subproof is completed by applying L43.
The subproof is completed by applying L44.