SIGNATURE MapByOSMap[dom, <, codomFrom, codomTo]

-- mapping on the codomain of a mapping

-- Parameter
SORT dom codomFrom codomTo
FUN < : dom ** dom -> bool
        -- total strict-order; in 
        --   ~(x < y) AND ~(y < x) => x = y
        -- should = represent semantic equality

IMPORT MapByOS[dom, <, codomFrom] ONLY map
       MapByOS[dom, <, codomTo]   ONLY map

FUN * : (codomFrom -> codomTo) ** map[dom,<,codomFrom] -> map[dom,<,codomTo]
        -- f * m
        -- apply f to all elements of codom of m