set L = Normal_forms_on A;
deffunc H1( Element of Normal_forms_on A, Element of Normal_forms_on A) -> Element of Normal_forms_on A = mi ($1 \/ $2);
consider j being BinOp of (Normal_forms_on A) such that
A1:
for x, y being Element of Normal_forms_on A holds j . (x,y) = H1(x,y)
from BINOP_1:sch 4();
deffunc H2( Element of Normal_forms_on A, Element of Normal_forms_on A) -> Element of Normal_forms_on A = mi ($1 ^ $2);
consider m being BinOp of (Normal_forms_on A) such that
A2:
for x, y being Element of Normal_forms_on A holds m . (x,y) = H2(x,y)
from BINOP_1:sch 4();
take
LattStr(# (Normal_forms_on A),j,m #)
; ( the carrier of LattStr(# (Normal_forms_on A),j,m #) = Normal_forms_on A & ( for B, C being Element of Normal_forms_on A holds
( the L_join of LattStr(# (Normal_forms_on A),j,m #) . (B,C) = mi (B \/ C) & the L_meet of LattStr(# (Normal_forms_on A),j,m #) . (B,C) = mi (B ^ C) ) ) )
thus
( the carrier of LattStr(# (Normal_forms_on A),j,m #) = Normal_forms_on A & ( for B, C being Element of Normal_forms_on A holds
( the L_join of LattStr(# (Normal_forms_on A),j,m #) . (B,C) = mi (B \/ C) & the L_meet of LattStr(# (Normal_forms_on A),j,m #) . (B,C) = mi (B ^ C) ) ) )
by A1, A2; verum