let q1, q2 be Element of MS; ( [frequency,q1] in octave MS & [frequency,q2] in octave MS implies q1 = q2 )
assume that
A1:
[frequency,q1] in octave MS
and
A2:
[frequency,q2] in octave MS
; q1 = q2
reconsider n1 = 1, n2 = 2 as Element of MS by Th20;
A3:
n1,n2 equiv frequency,q1
by A1, EQREL_1:18;
n1,n2 equiv frequency,q2
by A2, EQREL_1:18;
then
frequency,q2 equiv n1,n2
by Th22;
hence
q1 = q2
by A3, Th23, Th24; verum