let X be non empty TopSpace; :: thesis: for A1, A2 being Subset of X st ( A1 = A2 ` or A2 = A1 ` ) holds
A1,A2 constitute_a_decomposition
let A1, A2 be Subset of X; :: thesis: ( ( A1 = A2 ` or A2 = A1 ` ) implies A1,A2 constitute_a_decomposition )
assume ( A1 = A2 ` or A2 = A1 ` ) ; :: thesis: A1,A2 constitute_a_decomposition
then ( A1 misses A2 & A1 \/ A2 = [#] X ) by TDLAT_1:1, TDLAT_1:2;
hence A1,A2 constitute_a_decomposition by Def1; :: thesis: verum