let i be Element of NAT ; :: thesis: for K being non empty associative commutative multMagma
for a1, a2 being Element of K holds mlt (i |-> a1),(i |-> a2) = i |-> (a1 * a2)
let K be non empty associative commutative multMagma ; :: thesis: for a1, a2 being Element of K holds mlt (i |-> a1),(i |-> a2) = i |-> (a1 * a2)
let a1, a2 be Element of K; :: thesis: mlt (i |-> a1),(i |-> a2) = i |-> (a1 * a2)
thus mlt (i |-> a1),(i |-> a2) = a1 * (i |-> a2) by Th80
.= i |-> (a1 * a2) by Th66 ; :: thesis: verum