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.
Let x6 of type ο be given.
Apply and_def with
λ x7 x8 : ο → ο → ο . x8 (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6 ⟶ ∀ x9 : ο . (x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x9) ⟶ x9.
Assume H0:
∀ x7 : ο . (and (and (and (and (and x0 x1) x2) x3) x4) x5 ⟶ x6 ⟶ x7) ⟶ x7.
Let x7 of type ο be given.
Assume H1: x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7.
Apply H0 with
x7.
Assume H3: x6.
Apply unknownprop_caca72ca4ffee1c8dca675926193bc121ceebe999dc737cf8c2c0c2733e2c1d7 with
x0,
x1,
x2,
x3,
x4,
x5,
x7 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.
Assume H9: x5.
Apply H1 leaving 7 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 H9.
The subproof is completed by applying H3.