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 x being set st x in the Sorts of A . s holds
root-tree [x,s] is c-Term of A,V
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 x being set st x in the Sorts of A . s holds
root-tree [x,s] is c-Term of A,V
let A be MSAlgebra over S; :: thesis: for s being SortSymbol of S
for x being set st x in the Sorts of A . s holds
root-tree [x,s] is c-Term of A,V
let s be SortSymbol of S; :: thesis: for x being set st x in the Sorts of A . s holds
root-tree [x,s] is c-Term of A,V
let x be set ; :: thesis: ( x in the Sorts of A . s implies root-tree [x,s] is c-Term of A,V )
A1: ( the Sorts of A (\/) V) . s = ( the Sorts of A . s) \/ (V . s) by PBOOLE:def 4;
assume x in the Sorts of A . s ; :: thesis: root-tree [x,s] is c-Term of A,V
then x in ( the Sorts of A (\/) V) . s by A1, XBOOLE_0:def 3;
then reconsider xs = [x,s] as Terminal of (DTConMSA ( the Sorts of A (\/) V)) by MSAFREE:7;
root-tree xs in TS (DTConMSA ( the Sorts of A (\/) V)) ;
hence root-tree [x,s] is c-Term of A,V ; :: thesis: verum