let L be Lattice; :: thesis: 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 <> {} & f | B = g | B holds
FinJoin B,f = FinJoin B,g
let A be non empty set ; :: thesis: for B being Finite_Subset of A
for f, g being Function of A,the carrier of L st B <> {} & f | B = g | B holds
FinJoin B,f = FinJoin B,g
let B be Finite_Subset of A; :: thesis: for f, g being Function of A,the carrier of L st B <> {} & f | B = g | B holds
FinJoin B,f = FinJoin B,g
let f, g be Function of A,the carrier of L; :: thesis: ( B <> {} & f | B = g | B implies FinJoin B,f = FinJoin B,g )
assume that
A1: B <> {} and
A2: f | B = g | B ; :: thesis: FinJoin B,f = FinJoin B,g
f .: B = g .: B by A2, RELAT_1:201;
hence FinJoin B,f = FinJoin B,g by A1, SETWISEO:35; :: thesis: verum