let seq1, seq, seq1' be Real_Sequence; ( (seq1 /" seq) + (seq1' /" seq) = (seq1 + seq1') /" seq & (seq1 /" seq) - (seq1' /" seq) = (seq1 - seq1') /" seq )
thus (seq1 /" seq) + (seq1' /" seq) =
(seq1 + seq1') (#) (seq " )
by Th23
.=
(seq1 + seq1') /" seq
; (seq1 /" seq) - (seq1' /" seq) = (seq1 - seq1') /" seq
thus (seq1 /" seq) - (seq1' /" seq) =
(seq1 - seq1') (#) (seq " )
by Th28
.=
(seq1 - seq1') /" seq
; verum