let L be Lattice; :: thesis: for A being non empty set
for x being Element of A
for B being Finite_Subset of A
for f being Function of A,the carrier of L st x in B holds
f . x [= FinJoin B,f
let A be non empty set ; :: thesis: for x being Element of A
for B being Finite_Subset of A
for f being Function of A,the carrier of L st x in B holds
f . x [= FinJoin B,f
let x be Element of A; :: thesis: for B being Finite_Subset of A
for f being Function of A,the carrier of L st x in B holds
f . x [= FinJoin B,f
let B be Finite_Subset of A; :: thesis: for f being Function of A,the carrier of L st x in B holds
f . x [= FinJoin B,f
let f be Function of A,the carrier of L; :: thesis: ( x in B implies f . x [= FinJoin B,f )
assume x in B ; :: thesis: f . x [= FinJoin B,f
then (f . x) "\/" (FinJoin B,f) = FinJoin B,f by SETWISEO:31;
hence f . x [= FinJoin B,f by LATTICES:def 3; :: thesis: verum