let Y be non empty set ; :: thesis: for G being Subset of (PARTITIONS Y)
for A, B, C, D being a_partition of Y st G = {A,B,C,D} & A <> B & B <> C & B <> D holds
CompF (B,G) = (A '/\' C) '/\' D
let G be Subset of (PARTITIONS Y); :: thesis: for A, B, C, D being a_partition of Y st G = {A,B,C,D} & A <> B & B <> C & B <> D holds
CompF (B,G) = (A '/\' C) '/\' D
let A, B, C, D be a_partition of Y; :: thesis: ( G = {A,B,C,D} & A <> B & B <> C & B <> D implies CompF (B,G) = (A '/\' C) '/\' D )
{A,B,C,D} = {B,A,C,D} by ENUMSET1:65;
hence ( G = {A,B,C,D} & A <> B & B <> C & B <> D implies CompF (B,G) = (A '/\' C) '/\' D ) by Th7; :: thesis: verum