let A be non empty set ; for B being Finite_Subset of A
for L being 0_Lattice
for f, g being Function of A,the carrier of L st ( 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 L being 0_Lattice
for f, g being Function of A,the carrier of L st ( for x being Element of A st x in B holds
f . x [= g . x ) holds
FinJoin B,f [= FinJoin B,g
let L be 0_Lattice; for f, g being Function of A,the carrier of L st ( 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; ( ( for x being Element of A st x in B holds
f . x [= g . x ) implies FinJoin B,f [= FinJoin B,g )
assume A1:
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 Th70; verum