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 t being c-Term of A,V
for s being SortSymbol of S
for x being set st x in the Sorts of A . s & t = root-tree [x,s] holds
the_sort_of t = s
let V be non-empty ManySortedSet of the carrier of S; :: thesis: for A being MSAlgebra over S
for t being c-Term of A,V
for s being SortSymbol of S
for x being set st x in the Sorts of A . s & t = root-tree [x,s] holds
the_sort_of t = s
let A be MSAlgebra over S; :: thesis: for t being c-Term of A,V
for s being SortSymbol of S
for x being set st x in the Sorts of A . s & t = root-tree [x,s] holds
the_sort_of t = s
let t be c-Term of A,V; :: thesis: for s being SortSymbol of S
for x being set st x in the Sorts of A . s & t = root-tree [x,s] holds
the_sort_of t = s
let s be SortSymbol of S; :: thesis: for x being set st x in the Sorts of A . s & t = root-tree [x,s] holds
the_sort_of t = s
let x be set ; :: thesis: ( x in the Sorts of A . s & t = root-tree [x,s] implies the_sort_of t = s )
assume x in the Sorts of A . s ; :: thesis: ( not t = root-tree [x,s] or the_sort_of t = s )
then x in ( the Sorts of A . s) \/ (V . s) by XBOOLE_0:def 3;
then x in ( the Sorts of A (\/) V) . s by PBOOLE:def 4;
hence ( not t = root-tree [x,s] or the_sort_of t = s ) by Th14; :: thesis: verum