let D be non empty set ; :: thesis: for M being Matrix of D holds Len <*M*> = <*(len M)*>
let M be Matrix of D; :: thesis: Len <*M*> = <*(len M)*>
set F = <*M*>;
A1: len <*M*> = 1 by FINSEQ_1:57;
A2: <*M*> . 1 = M by FINSEQ_1:57;
A3: len <*M*> = len (Len <*M*>) by FINSEQ_1:def 18;
A4: dom (Len <*M*>) = Seg (len <*M*>) by FINSEQ_2:144;
1 in Seg 1 ;
then (Len <*M*>) . 1 = len (<*M*> . 1) by A1, A4, Def3;
hence Len <*M*> = <*(len M)*> by A1, A3, A2, FINSEQ_1:57; :: thesis: verum