let L be Lattice; for A being non empty set
for B being Finite_Subset of A
for f, g being Function of A,the carrier of L st B <> {} & ( for x being Element of A st x in B holds
f . x [= g . x ) holds
FinJoin B,f [= FinJoin B,g
let A be non empty set ; for B being Finite_Subset of A
for f, g being Function of A,the carrier of L st B <> {} & ( for x being Element of A st x in B holds
f . x [= g . x ) holds
FinJoin B,f [= FinJoin B,g
let B be Finite_Subset of A; for f, g being Function of A,the carrier of L st B <> {} & ( for x being Element of A st x in B holds
f . x [= g . x ) holds
FinJoin B,f [= FinJoin B,g
let f, g be Function of A,the carrier of L; ( B <> {} & ( for x being Element of A st x in B holds
f . x [= g . x ) implies FinJoin B,f [= FinJoin B,g )
assume that
A1:
B <> {}
and
A2:
for x being Element of A st x in B holds
f . x [= g . x
; FinJoin B,f [= FinJoin B,g
hence
FinJoin B,f [= FinJoin B,g
by A1, Th47; verum