let g, h be FinSequence of REAL ; :: thesis: ( dom g = Seg (card S) & ( for n being Nat st n in dom g holds
g . n = FDprobability (((canFS S) . n),s) ) & dom h = Seg (card S) & ( for n being Nat st n in dom h holds
h . n = FDprobability (((canFS S) . n),s) ) implies g = h )
assume that
A3: dom g = Seg (card S) and
A4: for n being Nat st n in dom g holds
g . n = FDprobability (((canFS S) . n),s) ; :: thesis: ( not dom h = Seg (card S) or ex n being Nat st
( n in dom h & not h . n = FDprobability (((canFS S) . n),s) ) or g = h )
assume that
A5: dom h = Seg (card S) and
A6: for n being Nat st n in dom h holds
h . n = FDprobability (((canFS S) . n),s) ; :: thesis: g = h

A7: now

let n be Nat; :: thesis: ( n in dom g implies g . n = h . n )
assume A8: n in dom g ; :: thesis: g . n = h . n
hence g . n = FDprobability (((canFS S) . n),s) by A4
.= h . n by A3, A5, A6, A8 ;
:: thesis: verum

end;

len g = card S by A3, FINSEQ_1:def 3
.= len h by A5, FINSEQ_1:def 3 ;
hence g = h by A7, FINSEQ_2:9; :: thesis: verum