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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 . In x4 x1x2 x4 = x3 x4)x0 x1 x2 = x0 x1 x3.
Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with λ x1 . 6869c.. x0 x1 (f9c5e.. x0 x1).
Let x1 of type ι be given.
Assume H1: ∀ x2 . In x2 x16869c.. x0 x2 (f9c5e.. x0 x2).
Apply Descr_Vo1_prop with 6869c.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2: ∀ x3 : ι → ο . 6869c.. x0 x1 x3x2.
Apply H2 with x0 x1 (f9c5e.. x0).
Apply unknownprop_7e1433f0d7534eb35553ba0ab0a1f0e9ad42c403c2045d379ba59305b2ddd888 with x0, x1, f9c5e.. x0.
The subproof is completed by applying H1.
Apply unknownprop_b770534102bad575dcc908ba2bd3be3cd352ae4c3095917d5f34873a1d6be083 with x0, x1.
The subproof is completed by applying H0.