Let x0 of type ι → ο be given.
Let x1 of type ι → ι → ι be given.
Assume H0: ∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3).
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Assume H1: x0 x2.
Assume H2: x0 x3.
Assume H3: x0 x4.
Assume H4: x0 x5.
Assume H5: x0 x6.
Assume H6: x0 x7.
Apply H0 with
x2,
x1 x3 (x1 x4 (x1 x5 (x1 x6 x7))) leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_d7ce6357a8261c6a4be44f579bedcb1c2d65cec14964ea078af8f02cc5aab85a with
x0,
x1,
x3,
x4,
x5,
x6,
x7 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 H5.
The subproof is completed by applying H6.