let n be Ordinal; :: thesis: for L being non trivial right_complementable Abelian add-associative right_zeroed associative commutative well-unital distributive left_zeroed doubleLoopStr
for p being Polynomial of n,L
for a being Element of L
for x being Function of n,L holds eval (p *' (a | n,L)),x = (eval p,x) * a
let L be non trivial right_complementable Abelian add-associative right_zeroed associative commutative well-unital distributive left_zeroed doubleLoopStr ; :: thesis: for p being Polynomial of n,L
for a being Element of L
for x being Function of n,L holds eval (p *' (a | n,L)),x = (eval p,x) * a
let p be Polynomial of n,L; :: thesis: for a being Element of L
for x being Function of n,L holds eval (p *' (a | n,L)),x = (eval p,x) * a
let a be Element of L; :: thesis: for x being Function of n,L holds eval (p *' (a | n,L)),x = (eval p,x) * a
let x be Function of n,L; :: thesis: eval (p *' (a | n,L)),x = (eval p,x) * a
thus eval (p *' (a | n,L)),x = (eval p,x) * (eval (a | n,L),x) by POLYNOM2:27
.= (eval p,x) * a by Th25 ; :: thesis: verum