Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H0: x0 = x1 ⟶ ∀ x5 : ο . x5.
Assume H1: x0 = x2 ⟶ ∀ x5 : ο . x5.
Assume H2: x1 = x2 ⟶ ∀ x5 : ο . x5.
Assume H3: x0 = x3 ⟶ ∀ x5 : ο . x5.
Assume H4: x1 = x3 ⟶ ∀ x5 : ο . x5.
Assume H5: x2 = x3 ⟶ ∀ x5 : ο . x5.
Assume H6: x0 = x4 ⟶ ∀ x5 : ο . x5.
Assume H7: x1 = x4 ⟶ ∀ x5 : ο . x5.
Assume H8: x2 = x4 ⟶ ∀ x5 : ο . x5.
Assume H9: x3 = x4 ⟶ ∀ x5 : ο . x5.
Apply unknownprop_eab190d6552dbda6c7d00c3e93c1ad9385698a8d73462a2a4e5795b67701610d with
u4,
SetAdjoin (SetAdjoin (UPair x0 x1) x2) x3,
x4 leaving 2 subgoals.
Apply unknownprop_cb75c47bae3a116273752c6fc8e52c777498313f2b5b4ef43d3ceb63348e2717 with
x0,
x1,
x2,
x3,
λ x5 . x5 = x4 ⟶ ∀ x6 : ο . x6,
x4 leaving 6 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
The subproof is completed by applying H10.
Let x5 of type ι → ι → ο be given.
Assume H11: x5 x4 x4.
The subproof is completed by applying H11.
Apply unknownprop_1284ca02145609bab9b058960e85f6a8edb5de0340c786fcfde3a88eb0d054c1 with
x0,
x1,
x2,
x3 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 H5.