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_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))), λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) x1 (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3)), 4ae4a.. (4ae4a.. 4a7ef..), λ x4 x5 . x5 = x2 leaving 2 subgoals.

The subproof is completed by applying unknownprop_1ee0c009b4e6cf9cf44a574cbd2de4b04802b7d08642b31b0d24534e89e0adc3.

The subproof is completed by applying unknownprop_38b5b92bfd131ef0428a8ee212f746419349b56c1e9077ab24b3c25647caace1.

Apply If_i_0 with 4ae4a.. (4ae4a.. 4a7ef..) = 4ae4a.. 4a7ef.., x1, If_i (4ae4a.. (4ae4a.. 4a7ef..) = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3, λ x4 x5 . x5 = x2 leaving 2 subgoals.

The subproof is completed by applying unknownprop_e0e602efce8c3fbbb791d74669e968feb76e9d28b29f3878aea98e1fe1efe584.

Let x4 of type ι → ι → ο be given.

The subproof is completed by applying H0.

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Proofgold Proof