let S be non empty non void ManySortedSign ; :: thesis: for V being V5 ManySortedSet of the carrier of S
for t being Term of S,V
for s being SortSymbol of S
for v being Element of V . s st t . {} = [v,s] holds
t = root-tree [v,s]
let V be V5 ManySortedSet of the carrier of S; :: thesis: for t being Term of S,V
for s being SortSymbol of S
for v being Element of V . s st t . {} = [v,s] holds
t = root-tree [v,s]
let t be Term of S,V; :: thesis: for s being SortSymbol of S
for v being Element of V . s st t . {} = [v,s] holds
t = root-tree [v,s]
let s be SortSymbol of S; :: thesis: for v being Element of V . s st t . {} = [v,s] holds
t = root-tree [v,s]
let x be Element of V . s; :: thesis: ( t . {} = [x,s] implies t = root-tree [x,s] )
set G = DTConMSA V;
reconsider a = [x,s] as Terminal of (DTConMSA V) by Lm3;
reconsider t = t as Element of TS (DTConMSA V) ;
( t . {} = a implies t = root-tree a ) by DTCONSTR:9;
hence ( t . {} = [x,s] implies t = root-tree [x,s] ) ; :: thesis: verum