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.
Let x9 of type ι be given.
Assume H8: x9 ∈ x0.
Assume H9: x1 = x2 ⟶ ∀ x10 : ο . x10.
Assume H10: x1 = x3 ⟶ ∀ x10 : ο . x10.
Assume H11: x2 = x3 ⟶ ∀ x10 : ο . x10.
Assume H12: x1 = x4 ⟶ ∀ x10 : ο . x10.
Assume H13: x2 = x4 ⟶ ∀ x10 : ο . x10.
Assume H14: x3 = x4 ⟶ ∀ x10 : ο . x10.
Assume H15: x1 = x5 ⟶ ∀ x10 : ο . x10.
Assume H16: x2 = x5 ⟶ ∀ x10 : ο . x10.
Assume H17: x3 = x5 ⟶ ∀ x10 : ο . x10.
Assume H18: x4 = x5 ⟶ ∀ x10 : ο . x10.
Assume H19: x1 = x6 ⟶ ∀ x10 : ο . x10.
Assume H20: x2 = x6 ⟶ ∀ x10 : ο . x10.
Assume H21: x3 = x6 ⟶ ∀ x10 : ο . x10.
Assume H22: x4 = x6 ⟶ ∀ x10 : ο . x10.
Assume H23: x5 = x6 ⟶ ∀ x10 : ο . x10.
Assume H24: x1 = x7 ⟶ ∀ x10 : ο . x10.
Assume H25: x2 = x7 ⟶ ∀ x10 : ο . x10.
Assume H26: x3 = x7 ⟶ ∀ x10 : ο . x10.
Assume H27: x4 = x7 ⟶ ∀ x10 : ο . x10.
Assume H28: x5 = x7 ⟶ ∀ x10 : ο . x10.
Assume H29: x6 = x7 ⟶ ∀ x10 : ο . x10.
Assume H30: x1 = x8 ⟶ ∀ x10 : ο . x10.
Assume H31: x2 = x8 ⟶ ∀ x10 : ο . x10.
Assume H32: x3 = x8 ⟶ ∀ x10 : ο . x10.
Assume H33: x4 = x8 ⟶ ∀ x10 : ο . x10.
Assume H34: x5 = x8 ⟶ ∀ x10 : ο . x10.
Assume H35: x6 = x8 ⟶ ∀ x10 : ο . x10.
Assume H36: x7 = x8 ⟶ ∀ x10 : ο . x10.
Assume H37: x1 = x9 ⟶ ∀ x10 : ο . x10.
Assume H38: x2 = x9 ⟶ ∀ x10 : ο . x10.
Assume H39: x3 = x9 ⟶ ∀ x10 : ο . x10.
Assume H40: x4 = x9 ⟶ ∀ x10 : ο . x10.
Assume H41: x5 = x9 ⟶ ∀ x10 : ο . x10.
Assume H42: x6 = x9 ⟶ ∀ x10 : ο . x10.
Assume H43: x7 = x9 ⟶ ∀ x10 : ο . x10.
Assume H44: x8 = x9 ⟶ ∀ x10 : ο . x10.
Apply unknownprop_fba79708a39155962b778db930af01bf3b440c82ca9f7fc2b68b6408eeed30a1 with
setminus x0 (Sing x9),
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8 leaving 36 subgoals.
The subproof is completed by applying L45.
The subproof is completed by applying L46.
The subproof is completed by applying L47.
The subproof is completed by applying L48.
The subproof is completed by applying L49.
The subproof is completed by applying L50.
The subproof is completed by applying L51.
The subproof is completed by applying L52.
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.
Apply unknownprop_20fce6fc7f2e036c1229cbf996632439eddb19cfae541105a83e5be9c65bc111 with
x0,
x9,
λ x10 x11 . atleastp u9 x11 leaving 2 subgoals.
The subproof is completed by applying H8.
Apply unknownprop_11c6158bd93dbd27daaa9a84a43404be6ccbf75f900b1e28dfa453e64ea6c96b with
u8,
setminus x0 (Sing x9),
x9 leaving 2 subgoals.
The subproof is completed by applying L53.
The subproof is completed by applying L54.