let i, j be Element of NAT ; :: thesis: for D being non empty set
for f being FinSequence of D st i in dom f & j in dom f holds
len (mid f,i,j) >= 1
let D be non empty set ; :: thesis: for f being FinSequence of D st i in dom f & j in dom f holds
len (mid f,i,j) >= 1
let f be FinSequence of D; :: thesis: ( i in dom f & j in dom f implies len (mid f,i,j) >= 1 )
A1: ( i <= j or j < i ) ;
assume i in dom f ; :: thesis: ( not j in dom f or len (mid f,i,j) >= 1 )
then A2: ( 1 <= i & i <= len f ) by FINSEQ_3:27;
assume j in dom f ; :: thesis: len (mid f,i,j) >= 1
then ( 1 <= j & j <= len f ) by FINSEQ_3:27;
then ( len (mid f,i,j) = (i -' j) + 1 or len (mid f,i,j) = (j -' i) + 1 ) by A2, A1, JORDAN3:27;
hence len (mid f,i,j) >= 1 by NAT_1:11; :: thesis: verum