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.
Assume H6:
80df3.. x1 x2 x3 x4 x5 x6.
Let x7 of type ο be given.
Assume H7:
8b6ad.. x1 x2 x5 x4 x3 ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ x1 x2 x6 ⟶ x1 x5 x6 ⟶ x1 x4 x6 ⟶ x1 x3 x6 ⟶ x7.
Apply H6 with
x7.
Assume H9: x2 = x6 ⟶ ∀ x8 : ο . x8.
Assume H10: x3 = x6 ⟶ ∀ x8 : ο . x8.
Assume H11: x4 = x6 ⟶ ∀ x8 : ο . x8.
Assume H12: x5 = x6 ⟶ ∀ x8 : ο . x8.
Assume H13: x1 x2 x6.
Assume H14: x1 x3 x6.
Assume H15: x1 x4 x6.
Assume H16: x1 x5 x6.
Apply H7 leaving 9 subgoals.
Apply unknownprop_89cfb12a954bfd063e2b6793d2c3bc204792a4d2cf346d6340e70987bc4e1e26 with
x0,
x1,
x5,
x4,
x3,
x2 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
The subproof is completed by applying H3.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
Apply unknownprop_eab9f404af4a5ed249d4b5c960caac8f18ad0c62c12ef05286e7d299188b29e4 with
x0,
x1,
x3,
x4,
x5,
x2 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H1.
Apply unknownprop_f1501571b0c8635600cb3f7be51d444c2a18f7cf6b74c2339ab198883bb98207 with
x0,
x1,
x2,
x3,
x4,
x5 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
The subproof is completed by applying H12.
The subproof is completed by applying H11.
The subproof is completed by applying H10.
The subproof is completed by applying H13.
The subproof is completed by applying H16.
The subproof is completed by applying H15.
The subproof is completed by applying H14.