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Proofgold Proof

pf
Let x0 of type ι(ιιο) → ιο be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → ι → ο . (∀ x4 . x4x1x2 x4 = x3 x4)x0 x1 x2 = x0 x1 x3.
Apply In_ind with λ x1 . f6068.. x0 x1 (In_rec_Vo1 x0 x1).
Let x1 of type ι be given.
Assume H1: ∀ x2 . x2x1f6068.. x0 x2 (In_rec_Vo1 x0 x2).
Apply Descr_Vo1_prop with f6068.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2: ∀ x3 : ι → ο . f6068.. x0 x1 x3x2.
Apply H2 with x0 x1 (In_rec_Vo1 x0).
Apply unknownprop_6b9d466c48459997b5943e2bfa8effee1803540eeebe30604246716ec482ccac with x0, x1, In_rec_Vo1 x0.
The subproof is completed by applying H1.
Apply unknownprop_4a87b3b2bcf10bd0616cd3b0459f4ca1014c4bcd0183902ba6aaa9f0fef066b0 with x0, x1.
The subproof is completed by applying H0.