Let x0 of type ο be given.
Let x1 of type ο be given.
Let x2 of type ο be given.
Let x3 of type ο be given.
Let x4 of type ο be given.
Let x5 of type ο be given.
Apply and_def with
λ x6 x7 : ο → ο → ο . x7 (and (and (and (and x0 x1) x2) x3) x4) x5 ⟶ ∀ x8 : ο . (x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x8) ⟶ x8.
Assume H0:
∀ x6 : ο . (and (and (and (and x0 x1) x2) x3) x4 ⟶ x5 ⟶ x6) ⟶ x6.
Let x6 of type ο be given.
Assume H1: x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6.
Apply H0 with
x6.
Assume H3: x5.
Apply unknownprop_bcfb235173b6e24d61b0900ebc9059688ec23fd5128404d7a36e3b666224a280 with
x0,
x1,
x2,
x3,
x4,
x6 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H4: x0.
Assume H5: x1.
Assume H6: x2.
Assume H7: x3.
Assume H8: x4.
Apply H1 leaving 6 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
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 H3.