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
FinMeet (B,f) [= f . x
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
FinMeet (B,f) [= f . x
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
FinMeet (B,f) [= f . x
let B be Finite_Subset of A; :: thesis: for f being Function of A, the carrier of L st x in B holds
FinMeet (B,f) [= f . x
let f be Function of A, the carrier of L; :: thesis: ( x in B implies FinMeet (B,f) [= f . x )
reconsider f9 = f as Function of A, the carrier of (L .:) ;
assume x in B ; :: thesis: FinMeet (B,f) [= f . x
then f9 . x [= FinJoin (B,f9) by Th43;
hence FinMeet (B,f) [= f . x by Th54; :: thesis: verum