Claim L0: ∀ x0 . 74e69.. x0 ⟶ ∀ x1 x2 . x0 = bf68c.. x1 x2 ⟶ and (74e69.. x1) (74e69.. x2)

Apply unknownprop_9eb52b34dc5ec3159c14c43cf9730f7233c1ae17392d54fc91e463c1c0c6ba1d with λ x0 . ∀ x1 x2 . x0 = bf68c.. x1 x2 ⟶ and (74e69.. x1) (74e69.. x2) leaving 3 subgoals.

Let x0 of type ι be given.

Let x1 of type ι be given.

Assume H0: 5e331.. = bf68c.. x0 x1.

Apply FalseE with and (74e69.. x0) (74e69.. x1).

Apply unknownprop_951e3ef812229b5945a39a7fa79f4fd40c15277c7d728e18721eb777036d91be with x0, x1.

The subproof is completed by applying H0.

Let x0 of type ι be given.

Let x1 of type ι be given.

Assume H0: 74e69.. x0.

Assume H1: ∀ x2 x3 . x0 = bf68c.. x2 x3 ⟶ and (74e69.. x2) (74e69.. x3).

Assume H2: 74e69.. x1.

Assume H3: ∀ x2 x3 . x1 = bf68c.. x2 x3 ⟶ and (74e69.. x2) (74e69.. x3).

Let x2 of type ι be given.

Let x3 of type ι be given.

Assume H4: a3eb9.. x0 x1 = bf68c.. x2 x3.

Apply FalseE with and (74e69.. x2) (74e69.. x3).

Apply unknownprop_856b8bfadc699ad231b4ff87ec1e03728d77f11011b06095d14ff77ccdcd01b1 with x0, x1, x2, x3.

The subproof is completed by applying H4.

Let x0 of type ι be given.

Let x1 of type ι be given.

Assume H0: 74e69.. x0.

Assume H1: ∀ x2 x3 . x0 = bf68c.. x2 x3 ⟶ and (74e69.. x2) (74e69.. x3).

Assume H2: 74e69.. x1.

Assume H3: ∀ x2 x3 . x1 = bf68c.. x2 x3 ⟶ and (74e69.. x2) (74e69.. x3).

Let x2 of type ι be given.

Let x3 of type ι be given.

Assume H4: bf68c.. x0 x1 = bf68c.. x2 x3.

Apply unknownprop_432e2c1c265f7e33a9860d434376e8f246f661a5f0846be4ef608e5e6cdcb57b 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.

Assume H1: 74e69.. (bf68c.. x0 x1).

Apply L0 with bf68c.. x0 x1, x0, x1 leaving 2 subgoals.

The subproof is completed by applying H1.

Let x2 of type ι → ι → ο be given.

Assume H2: x2 (bf68c.. x0 x1) (bf68c.. x0 x1).

The subproof is completed by applying H2.

■

Proofgold Proof