set p = |[0,0]|;
set q = |[1,1]|;
set f = <*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*>;
A1: |[0,0]| `2 = 0 by EUCLID:52;
A2: |[1,1]| `1 = 1 by EUCLID:52;
A3: |[1,1]| `2 = 1 by EUCLID:52;
|[0,0]| `1 = 0 by EUCLID:52;
then <*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*> is being_S-Seq by A1, A2, A3, TOPREAL3:34;
then L~ <*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*> is being_S-P_arc ;
hence ex b₁ being Subset of (TOP-REAL 2) st b₁ is being_S-P_arc ; :: thesis: verum