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
A4: dom g = Seg (card S) and
A5: 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
A6: dom h = Seg (card S) and
A7: for n being Nat st n in dom h holds
h . n = FDprobability (((canFS S) . n),s) ; :: thesis: g = h

A8: now :: thesis: for n being Nat st n in dom g holds
g . n = h . n

let n be Nat; :: thesis: ( n in dom g implies g . n = h . n )
assume A9: n in dom g ; :: thesis: g . n = h . n
hence g . n = FDprobability (((canFS S) . n),s) by A5
.= h . n by A4, A6, A7, A9 ;
:: thesis: verum

end;

len g = card S by A4, FINSEQ_1:def 3
.= len h by A6, FINSEQ_1:def 3 ;
hence g = h by A8, FINSEQ_2:9; :: thesis: verum