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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: bc82c.. x0 x1 = bc82c.. x2 x1.
Claim L4: bc82c.. x1 x0 = bc82c.. x1 x2
Apply unknownprop_443bf25288cf39bc78395680f7fe50ad1a2a509c594b439821412f6af4f99866 with x1, x0, λ x3 x4 . x4 = bc82c.. x1 x2 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Apply unknownprop_443bf25288cf39bc78395680f7fe50ad1a2a509c594b439821412f6af4f99866 with x1, x2, λ x3 x4 . bc82c.. x0 x1 = x4 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_dff6e8fda85df9e92da1fa7de32e7db4e93608d23c35200508d6d4985bb05bac with x1, x0, x2 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying L4.