let a, c be Element of L; :: thesis: ( ex y being FinSequence of the carrier of L st
( len y = len (SgmX (RelIncl n),(support b)) & a = Product y & ( for i being Element of NAT st 1 <= i & i <= len y holds
y /. i = (power L) . ((x * (SgmX (RelIncl n),(support b))) /. i),((b * (SgmX (RelIncl n),(support b))) /. i) ) ) & ex y being FinSequence of the carrier of L st
( len y = len (SgmX (RelIncl n),(support b)) & c = Product y & ( for i being Element of NAT st 1 <= i & i <= len y holds
y /. i = (power L) . ((x * (SgmX (RelIncl n),(support b))) /. i),((b * (SgmX (RelIncl n),(support b))) /. i) ) ) implies a = c )
assume that
A4: ex y1 being FinSequence of the carrier of L st
( len y1 = len (SgmX (RelIncl n),(support b)) & a = Product y1 & ( for i being Element of NAT st 1 <= i & i <= len y1 holds
y1 /. i = (power L) . ((x * (SgmX (RelIncl n),(support b))) /. i),((b * (SgmX (RelIncl n),(support b))) /. i) ) ) and
A5: ex y2 being FinSequence of the carrier of L st
( len y2 = len (SgmX (RelIncl n),(support b)) & c = Product y2 & ( for i being Element of NAT st 1 <= i & i <= len y2 holds
y2 /. i = (power L) . ((x * (SgmX (RelIncl n),(support b))) /. i),((b * (SgmX (RelIncl n),(support b))) /. i) ) ) ; :: thesis: a = c
consider y1 being FinSequence of the carrier of L such that
A6: ( len y1 = len (SgmX (RelIncl n),(support b)) & Product y1 = a & ( for i being Element of NAT st 1 <= i & i <= len y1 holds
y1 /. i = (power L) . ((x * (SgmX (RelIncl n),(support b))) /. i),((b * (SgmX (RelIncl n),(support b))) /. i) ) ) by A4;
consider y2 being FinSequence of the carrier of L such that
A7: ( len y2 = len (SgmX (RelIncl n),(support b)) & Product y2 = c & ( for i being Element of NAT st 1 <= i & i <= len y2 holds
y2 /. i = (power L) . ((x * (SgmX (RelIncl n),(support b))) /. i),((b * (SgmX (RelIncl n),(support b))) /. i) ) ) by A5;
set S = SgmX (RelIncl n),(support b);

now

let i be Nat; :: thesis: ( 1 <= i & i <= len y1 implies y1 . i = y2 . i )
assume A8: ( 1 <= i & i <= len y1 ) ; :: thesis: y1 . i = y2 . i
then A9: ( i in Seg (len y1) & i in Seg (len y2) ) by A6, A7, FINSEQ_1:3;
then A10: ( i in dom y1 & i in dom y2 ) by FINSEQ_1:def 3;
hence y1 . i = y1 /. i by PARTFUN1:def 8
.= (power L) . ((x * (SgmX (RelIncl n),(support b))) /. i),((b * (SgmX (RelIncl n),(support b))) /. i) by A6, A8, A9
.= y2 /. i by A6, A7, A8, A9
.= y2 . i by A10, PARTFUN1:def 8 ;
:: thesis: verum

end;

hence a = c by A6, A7, FINSEQ_1:18; :: thesis: verum