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

.= len h by A6, FINSEQ_1:def 3 ;

hence g = h by A8, FINSEQ_2:9; :: thesis: verum

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

len g =
card S
by A4, FINSEQ_1:def 3
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;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

.= len h by A6, FINSEQ_1:def 3 ;

hence g = h by A8, FINSEQ_2:9; :: thesis: verum