reconsider MM = MetrStruct(# the carrier of M,the distance of M #) as MetrSpace by Lm1;
take MM ; :: thesis: ( the carrier of MM c= the carrier of M & ( for x, y being Point of MM holds the distance of MM . x,y = the distance of M . x,y ) )
thus the carrier of MM c= the carrier of M ; :: thesis: for x, y being Point of MM holds the distance of MM . x,y = the distance of M . x,y
let x, y be Point of MM; :: thesis: the distance of MM . x,y = the distance of M . x,y
thus the distance of MM . x,y = the distance of M . x,y ; :: thesis: verum