Let x0 of type ι → ο be given.
Let x1 of type ι → ο be given.
Let x2 of type ι be given.
Let x3 of type ι → ο be given.
Assume H1:
∀ x4 x5 . x0 x4 ⟶ x1 x5 ⟶ x3 (cfc98.. x4 x5).
Apply H0 with
x3 x2.
Let x4 of type ι be given.
Assume H2:
(λ x5 . ∃ x6 . and (and (x0 x5) (x1 x6)) (x2 = cfc98.. x5 x6)) x4.
Apply H2 with
x3 x2.
Let x5 of type ι be given.
Assume H3:
(λ x6 . and (and (x0 x4) (x1 x6)) (x2 = cfc98.. x4 x6)) x5.
Apply H3 with
x3 x2.
Assume H4:
and (x0 x4) (x1 x5).
Apply H4 with
x2 = cfc98.. x4 x5 ⟶ x3 x2.
Assume H5: x0 x4.
Assume H6: x1 x5.
Apply H7 with
λ x6 x7 . x3 x7.
Apply H1 with
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying H6.