let frequency be Element of RAT_Music; :: according to MUSIC_S1:def 46 :: thesis: ex o being Element of RAT_Music st [frequency,o] in octave RAT_Music
consider fr, qr being positive Rational such that
A1: fr = frequency and
qr = 2 * fr and
A2: [fr,qr] in octave RAT_Music by Th43;
( fr is Element of RAT_Music & qr is Element of RAT_Music ) by Th2;
hence ex o being Element of RAT_Music st [frequency,o] in octave RAT_Music by A1, A2; :: thesis: verum