let n be Element of NAT ; :: thesis: for s1, s2, s3 being FinSequence st len s1 = n & len s2 = n & len s3 = n holds
<*s1,s2,s3*> is tabular
let s1, s2, s3 be FinSequence; :: thesis: ( len s1 = n & len s2 = n & len s3 = n implies <*s1,s2,s3*> is tabular )
assume that
A1: len s1 = n and
A2: len s2 = n and
A3: len s3 = n ; :: thesis: <*s1,s2,s3*> is tabular

now

take n = n; :: thesis: for x being set st x in rng <*s1,s2,s3*> holds
ex r being FinSequence st
( x = r & len r = n )
let x be set ; :: thesis: ( x in rng <*s1,s2,s3*> implies ex r being FinSequence st
( x = r & len r = n ) )
assume x in rng <*s1,s2,s3*> ; :: thesis: ex r being FinSequence st
( x = r & len r = n )
then A4: x in {s1,s2,s3} by FINSEQ_2:148;
then reconsider r = x as FinSequence by ENUMSET1:def 1;
take r = r; :: thesis: ( x = r & len r = n )
thus ( x = r & len r = n ) by A1, A2, A3, A4, ENUMSET1:def 1; :: thesis: verum

end;

hence <*s1,s2,s3*> is tabular by MATRIX_1:def 1; :: thesis: verum