let OAS be OAffinSpace; :: thesis: for f being Permutation of the carrier of (Lambda OAS) st f is_DIL_of Lambda OAS holds
ex f9 being Permutation of the carrier of OAS st
( f = f9 & f9 is dilatation )
let f be Permutation of the carrier of (Lambda OAS); :: thesis: ( f is_DIL_of Lambda OAS implies ex f9 being Permutation of the carrier of OAS st
( f = f9 & f9 is dilatation ) )
A1: Lambda OAS = AffinStruct(# the carrier of OAS,(lambda the CONGR of OAS) #) by DIRAF:def 2;
then reconsider f9 = f as Permutation of the carrier of OAS ;
assume f is_DIL_of Lambda OAS ; :: thesis: ex f9 being Permutation of the carrier of OAS st
( f = f9 & f9 is dilatation )
then A2: f is_FormalIz_of the CONGR of (Lambda OAS) ;
take f9 ; :: thesis: ( f = f9 & f9 is dilatation )
thus ( f = f9 & f9 is dilatation ) by A2, A1; :: thesis: verum