let i, j be Nat; :: thesis: for K being Field
for R1, S1 being Element of i -tuples_on the carrier of K
for R2, S2 being Element of j -tuples_on the carrier of K holds Sum (mlt (R1 ^ R2),(S1 ^ S2)) = (Sum (mlt R1,S1)) + (Sum (mlt R2,S2))
let K be Field; :: thesis: for R1, S1 being Element of i -tuples_on the carrier of K
for R2, S2 being Element of j -tuples_on the carrier of K holds Sum (mlt (R1 ^ R2),(S1 ^ S2)) = (Sum (mlt R1,S1)) + (Sum (mlt R2,S2))
let R1, S1 be Element of i -tuples_on the carrier of K; :: thesis: for R2, S2 being Element of j -tuples_on the carrier of K holds Sum (mlt (R1 ^ R2),(S1 ^ S2)) = (Sum (mlt R1,S1)) + (Sum (mlt R2,S2))
let R2, S2 be Element of j -tuples_on the carrier of K; :: thesis: Sum (mlt (R1 ^ R2),(S1 ^ S2)) = (Sum (mlt R1,S1)) + (Sum (mlt R2,S2))
mlt (R1 ^ R2),(S1 ^ S2) = (mlt R1,S1) ^ (mlt R2,S2) by FINSEQOP:12;
hence Sum (mlt (R1 ^ R2),(S1 ^ S2)) = (Sum (mlt R1,S1)) + (Sum (mlt R2,S2)) by RLVECT_1:58; :: thesis: verum