Let x0 of type ι be given.
Let x1 of type ο be given.
Assume H1: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ (x2 = x3 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x4 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x4 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x6 = x7 ⟶ ∀ x8 : ο . x8) ⟶ x1.
Apply unknownprop_611d05f3c0e0aff033700ccf72b7ceaf4160dd0bd5dde16fbd4a43684d4061b2 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying L2.
Let x2 of type ι be given.
Assume H3: x2 ∈ x0.
Let x3 of type ι be given.
Assume H4: x3 ∈ x0.
Let x4 of type ι be given.
Assume H5: x4 ∈ x0.
Let x5 of type ι be given.
Assume H6: x5 ∈ x0.
Let x6 of type ι be given.
Assume H7: x6 ∈ x0.
Assume H8: x2 = x3 ⟶ ∀ x7 : ο . x7.
Assume H9: x2 = x4 ⟶ ∀ x7 : ο . x7.
Assume H10: x2 = x5 ⟶ ∀ x7 : ο . x7.
Assume H11: x2 = x6 ⟶ ∀ x7 : ο . x7.
Assume H12: x3 = x4 ⟶ ∀ x7 : ο . x7.
Assume H13: x3 = x5 ⟶ ∀ x7 : ο . x7.
Assume H14: x3 = x6 ⟶ ∀ x7 : ο . x7.
Assume H15: x4 = x5 ⟶ ∀ x7 : ο . x7.
Assume H16: x4 = x6 ⟶ ∀ x7 : ο . x7.
Assume H17: x5 = x6 ⟶ ∀ x7 : ο . x7.
Apply xm with
∀ x7 : ο . (∀ x8 . x8 ∈ x0 ⟶ (x2 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x8 ⟶ ∀ x9 : ο . x9) ⟶ x7) ⟶ x7,
x1 leaving 2 subgoals.
Assume H18: ∀ x7 : ο . (∀ x8 . x8 ∈ x0 ⟶ (x2 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x8 ⟶ ∀ x9 : ο . x9) ⟶ x7) ⟶ x7.
Apply H18 with
x1.
Let x7 of type ι be given.
Assume H19: x7 ∈ x0.
Assume H20: x2 = x7 ⟶ ∀ x8 : ο . x8.
Assume H21: x3 = x7 ⟶ ∀ x8 : ο . x8.
Assume H22: x4 = x7 ⟶ ∀ x8 : ο . x8.
Assume H23: x5 = x7 ⟶ ∀ x8 : ο . x8.
Assume H24: ... ⟶ ∀ x8 : ο . x8.