let N be Nat; :: thesis: for q, r being Real
for seq being Real_Sequence of N holds (r * q) * seq = r * (q * seq)
let q, r be Real; :: thesis: for seq being Real_Sequence of N holds (r * q) * seq = r * (q * seq)
let seq be Real_Sequence of N; :: thesis: (r * q) * seq = r * (q * seq)
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: ((r * q) * seq) . n = (r * (q * seq)) . n
thus ((r * q) * seq) . n = (r * q) * (seq . n) by Th5
.= r * (q * (seq . n)) by RLVECT_1:def 7
.= r * ((q * seq) . n) by Th5
.= (r * (q * seq)) . n by Th5 ; :: thesis: verum