let A, B, C be Point of (TOP-REAL 2); for a, b, r being Real st A,B,C is_a_triangle & A in circle (a,b,r) & B in circle (a,b,r) holds
r is positive
let a, b, r be Real; ( A,B,C is_a_triangle & A in circle (a,b,r) & B in circle (a,b,r) implies r is positive )
assume that
A1:
A,B,C is_a_triangle
and
A2:
( A in circle (a,b,r) & B in circle (a,b,r) )
; r is positive
A3:
A,B,C are_mutually_distinct
by A1, EUCLID_6:20;
assume
not r is positive
; contradiction