Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2.
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.
Let x10 of type ι be given.
Assume H9: x10 ∈ x0.
Let x11 of type ι be given.
Assume H10: x11 ∈ x0.
Assume H11:
33f3e.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11.
Let x12 of type ο be given.
Assume H12:
1668d.. x1 x9 x8 x4 x5 x7 x6 x3 x2 x10 ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x1 x9 x11 ⟶ not (x1 x8 x11) ⟶ not (x1 x4 x11) ⟶ x1 x5 x11 ⟶ not (x1 x7 x11) ⟶ not (x1 x6 x11) ⟶ not (x1 x3 x11) ⟶ x1 x2 x11 ⟶ not (x1 x10 x11) ⟶ x12.
Apply H11 with
x12.
Assume H13:
1668d.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10.
Assume H14: x2 = x11 ⟶ ∀ x13 : ο . x13.
Assume H15: x3 = x11 ⟶ ∀ x13 : ο . x13.
Assume H16: x4 = x11 ⟶ ∀ x13 : ο . x13.
Assume H17: x5 = x11 ⟶ ∀ x13 : ο . x13.
Assume H18: x6 = x11 ⟶ ∀ x13 : ο . x13.
Assume H19: x7 = x11 ⟶ ∀ x13 : ο . x13.
Assume H20: x8 = x11 ⟶ ∀ x13 : ο . x13.
Assume H21: x9 = x11 ⟶ ∀ x13 : ο . x13.
Assume H22: x10 = x11 ⟶ ∀ x13 : ο . x13.
Assume H23: x1 x2 x11.
Assume H24:
not (x1 x3 x11).
Assume H25:
not (x1 x4 x11).
Assume H26: x1 x5 x11.
Assume H27:
not (x1 x6 x11).
Assume H28:
not (x1 x7 x11).
Assume H29:
not (x1 x8 x11).
Assume H30: x1 x9 x11.
Assume H31:
not (x1 x10 x11).
Apply H12 leaving 19 subgoals.
Apply unknownprop_dbcdf2576b06ca84dc1e58b1b3bc1e34f91a369c3a3a70b925ae823aff4fa652 with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8,
x9,
x10 leaving 11 subgoals.