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_3a727fa768d5525d8195bdc93993ff4ea68fc9d53a8aef656546df8c698dedd5 with
x2,
λ x4 x5 . bc82c.. (bc82c.. x0 (bc82c.. x1 (f4dc0.. x2))) (bc82c.. x4 x3) = bc82c.. x0 (bc82c.. x1 x3) leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_72a10a6ff43a547508a4a6b39d7c77eb015a493c1fc838eccd7000515bcd21ff with
x0,
x1,
f4dc0.. x2,
x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_8fbd0c2b48e78882e15936a0ad5f4a3c5af2cb37d9320d8cb210a91462e202ca with
x2.
The subproof is completed by applying H2.
The subproof is completed by applying H3.