let B1, B2 be non empty strict full subcategory of non empty strict semi-functional full para-functional set-id-inheriting concrete carrier-underlaid lattice-wise with_complete_lattices with_all_isomorphisms ; :: thesis: ( ( for a being object of holds
( a is object of iff latt a is algebraic ) ) & ( for a being object of holds
( a is object of iff latt a is algebraic ) ) implies B1 = B2 )
assume that
A3: for a being object of holds
( a is object of iff S₁[a] ) and
A4: for a being object of holds
( a is object of iff S₁[a] ) ; :: thesis: B1 = B2
AltCatStr(# the carrier of B1,the Arrows of B1,the Comp of B1 #) = AltCatStr(# the carrier of B2,the Arrows of B2,the Comp of B2 #) from YELLOW20:sch 3(A3, A4);
hence B1 = B2 ; :: thesis: verum