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.

Let x4 of type ι be given.

Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))), λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) x1 (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))), 4ae4a.. (4ae4a.. 4a7ef..), λ x5 x6 . x6 = x2 leaving 2 subgoals.

The subproof is completed by applying unknownprop_789652ebe6bd3fa25bd01af35c5dda6651724e352ff77c589b1e478a53c425d7.

The subproof is completed by applying unknownprop_38b5b92bfd131ef0428a8ee212f746419349b56c1e9077ab24b3c25647caace1.

The subproof is completed by applying unknownprop_e0e602efce8c3fbbb791d74669e968feb76e9d28b29f3878aea98e1fe1efe584.

Let x5 of type ι → ι → ο be given.

The subproof is completed by applying H0.

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Proofgold Proof