let L be non empty RelStr ; :: thesis: id L is infs-preserving

let X be Subset of L; :: according to WAYBEL_0:def 32 :: thesis: id L preserves_inf_of X

set f = id L;

assume ex_inf_of X,L ; :: according to WAYBEL_0:def 30 :: thesis: ( ex_inf_of (id L) .: X,L & "/\" (((id L) .: X),L) = (id L) . ("/\" (X,L)) )

hence ex_inf_of (id L) .: X,L by FUNCT_1:92; :: thesis: "/\" (((id L) .: X),L) = (id L) . ("/\" (X,L))

(id L) .: X = X by FUNCT_1:92;

hence "/\" (((id L) .: X),L) = (id L) . ("/\" (X,L)) ; :: thesis: verum

let X be Subset of L; :: according to WAYBEL_0:def 32 :: thesis: id L preserves_inf_of X

set f = id L;

assume ex_inf_of X,L ; :: according to WAYBEL_0:def 30 :: thesis: ( ex_inf_of (id L) .: X,L & "/\" (((id L) .: X),L) = (id L) . ("/\" (X,L)) )

hence ex_inf_of (id L) .: X,L by FUNCT_1:92; :: thesis: "/\" (((id L) .: X),L) = (id L) . ("/\" (X,L))

(id L) .: X = X by FUNCT_1:92;

hence "/\" (((id L) .: X),L) = (id L) . ("/\" (X,L)) ; :: thesis: verum