Let x0 of type ι → ι → ο be given.
Assume H0: ∀ x1 x2 . x0 x1 x2 ⟶ x0 x2 x1.
Assume H2:
not (or (∃ x1 . and (x1 ⊆ u9) (and (equip u3 x1) (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ x0 x2 x3))) (∃ x1 . and (x1 ⊆ u9) (and (equip u4 x1) (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ not (x0 x2 x3))))).
Let x1 of type ι be given.
Let x2 of type ο be given.
Assume H4:
∀ x3 . x3 ∈ u9 ⟶ ∀ x4 . x4 ∈ u9 ⟶ ∀ x5 . x5 ∈ u9 ⟶ ∀ x6 . x6 ∈ u9 ⟶ (x1 = x3 ⟶ ∀ x7 : ο . x7) ⟶ (x1 = x4 ⟶ ∀ x7 : ο . x7) ⟶ (x1 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x1 = x6 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x4 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x6 ⟶ ∀ x7 : ο . x7) ⟶ (x4 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x4 = x6 ⟶ ∀ x7 : ο . x7) ⟶ (x5 = x6 ⟶ ∀ x7 : ο . x7) ⟶ x0 x1 x3 ⟶ x0 x1 x4 ⟶ x0 x1 x5 ⟶ not (x0 x3 x4) ⟶ not (x0 x3 x5) ⟶ not (x0 x4 x5) ⟶ (∀ x7 . x7 ∈ u9 ⟶ x0 x1 x7 ⟶ x7 ∈ SetAdjoin (SetAdjoin (UPair x1 x3) x4) x5) ⟶ x0 x6 x3 ⟶ x0 x6 x4 ⟶ x2.
Apply unknownprop_15d48b0d93044e45e1d5f0b67d2878c4ac013f81cd695d89157633dd4a764e14 with
x0,
x1,
x2 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Assume H8: x1 = x3 ⟶ ∀ x6 : ο . x6.
Assume H9: x1 = x4 ⟶ ∀ x6 : ο . x6.
Assume H10: x1 = x5 ⟶ ∀ x6 : ο . x6.
Assume H11: x3 = x4 ⟶ ∀ x6 : ο . x6.
Assume H12: x3 = x5 ⟶ ∀ x6 : ο . x6.
Assume H13: x4 = x5 ⟶ ∀ x6 : ο . x6.
Assume H14: x0 x1 x3.
Assume H15: x0 x1 x4.
Assume H16: x0 x1 x5.
Assume H17:
not (x0 x3 x4).
Assume H18:
not (x0 x3 x5).
Assume H19:
not (x0 x4 x5).
Apply unknownprop_5df8c11eede12b7d829e2a0b95c8033f28b954d28a1a477c3fa227324f16bb6c with
x0,
x3,
x1,
x2 leaving 7 subgoals.