consider r being positive real number , o being Point of (TOP-REAL 2), y being Point of (Tcircle (o,r));
let S be being_simple_closed_curve SubSpace of TOP-REAL 2; :: thesis: for x being Point of S holds INT.Group , pi_1 (S,x) are_isomorphic
let x be Point of S; :: thesis: INT.Group , pi_1 (S,x) are_isomorphic
( INT.Group , pi_1 ((Tcircle (o,r)),y) are_isomorphic & pi_1 ((Tcircle (o,r)),y), pi_1 (S,x) are_isomorphic ) by Lm16, TOPALG_3:35, TOPREALB:11;
hence INT.Group , pi_1 (S,x) are_isomorphic by GROUP_6:78; :: thesis: verum