Apply unknownprop_9eb52b34dc5ec3159c14c43cf9730f7233c1ae17392d54fc91e463c1c0c6ba1d with
λ x0 . ∀ x1 x2 . x0 = a3eb9.. x1 x2 ⟶ and (74e69.. x1) (74e69.. x2) leaving 3 subgoals.
Let x0 of type ι be given.
Let x1 of type ι be given.
Apply FalseE with
and (74e69.. x0) (74e69.. x1).
Apply unknownprop_112da44b75efcdc251767c8f8619fc43c6b883afd5ac71e5854bf36b62571f0c with
x0,
x1.
The subproof is completed by applying H0.
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply unknownprop_1f81fbea8647063ecd1729d03bf27a5327e4a018cc4ad3e99f64b38027811c93 with
x0,
x1,
x2,
x3,
and (74e69.. x2) (74e69.. x3) leaving 2 subgoals.
The subproof is completed by applying H4.
Assume H5: x0 = x2.
Assume H6: x1 = x3.
Apply andI with
74e69.. x2,
74e69.. x3 leaving 2 subgoals.
Apply H5 with
λ x4 x5 . 74e69.. x4.
The subproof is completed by applying H0.
Apply H6 with
λ x4 x5 . 74e69.. x4.
The subproof is completed by applying H2.
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply FalseE with
and (74e69.. x2) (74e69.. x3).
Apply unknownprop_856b8bfadc699ad231b4ff87ec1e03728d77f11011b06095d14ff77ccdcd01b1 with
x2,
x3,
x0,
x1.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H4 with λ x5 x6 . x4 x6 x5.
Let x0 of type ι be given.
Let x1 of type ι be given.
Apply L0 with
a3eb9.. x0 x1,
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H2.