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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: 80242.. x1.
Assume H2: 80242.. x2.
Assume H3: 099f3.. (bc82c.. x0 x1) (bc82c.. x2 x1).
Claim L4: bc82c.. (bc82c.. x0 x1) (f4dc0.. x1) = x0
Apply unknownprop_2dabdcbdf62eb35e893b1da7cf9ea26462f4b63bcb37cf7a3640d2d2117f04a1 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Claim L5: bc82c.. (bc82c.. x2 x1) (f4dc0.. x1) = x2
Apply unknownprop_2dabdcbdf62eb35e893b1da7cf9ea26462f4b63bcb37cf7a3640d2d2117f04a1 with x2, x1 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
Apply L4 with λ x3 x4 . 099f3.. x3 x2.
Apply L5 with λ x3 x4 . 099f3.. (bc82c.. (bc82c.. x0 x1) (f4dc0.. x1)) x3.
Apply unknownprop_b751afd4b96b439a72771c5e6447c46f37e6851a11a9a372baaf45b11a370b67 with bc82c.. x0 x1, f4dc0.. x1, bc82c.. x2 x1 leaving 4 subgoals.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_8fbd0c2b48e78882e15936a0ad5f4a3c5af2cb37d9320d8cb210a91462e202ca with x1.
The subproof is completed by applying H1.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with x2, x1 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
The subproof is completed by applying H3.