let S be non empty non void ManySortedSign ; :: thesis: for V being V16() ManySortedSet of the carrier of S
for A being MSAlgebra of 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 V16() ManySortedSet of the carrier of S; :: thesis: for A being MSAlgebra of 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 of 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 7;
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