let S be non empty non void ManySortedSign ; :: thesis: for V being non-empty ManySortedSet of the carrier of S
for A being MSAlgebra over S
for s being SortSymbol of S
for v being Element of V . s holds the_sort_of (v -term A) = s
let V be non-empty ManySortedSet of the carrier of S; :: thesis: for A being MSAlgebra over S
for s being SortSymbol of S
for v being Element of V . s holds the_sort_of (v -term A) = s
let A be MSAlgebra over S; :: thesis: for s being SortSymbol of S
for v being Element of V . s holds the_sort_of (v -term A) = s
let s be SortSymbol of S; :: thesis: for v being Element of V . s holds the_sort_of (v -term A) = s
let v be Element of V . s; :: thesis: the_sort_of (v -term A) = s
( the Sorts of A (\/) V) . s = ( the Sorts of A . s) \/ (V . s) by PBOOLE:def 4;
then v in ( the Sorts of A (\/) V) . s by XBOOLE_0:def 3;
hence the_sort_of (v -term A) = s by Th14; :: thesis: verum