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 . {} = [x,s] holds
t = root-tree [x,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 . {} = [x,s] holds
t = root-tree [x,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 . {} = [x,s] holds
t = root-tree [x,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 . {} = [x,s] holds
t = root-tree [x,s]
let s be SortSymbol of S; :: thesis: for x being set st x in the Sorts of A . s & t . {} = [x,s] holds
t = root-tree [x,s]
let x be set ; :: thesis: ( x in the Sorts of A . s & t . {} = [x,s] implies t = root-tree [x,s] )
set G = DTConMSA ( the Sorts of A (\/) V);
reconsider t = t as Element of TS (DTConMSA ( the Sorts of A (\/) V)) ;
assume x in the Sorts of A . s ; :: thesis: ( not t . {} = [x,s] or t = root-tree [x,s] )
then reconsider a = [x,s] as Terminal of (DTConMSA ( the Sorts of A (\/) V)) by Lm4;
( t . {} = a implies t = root-tree a ) by DTCONSTR:9;
hence ( not t . {} = [x,s] or t = root-tree [x,s] ) ; :: thesis: verum