let n be Nat; :: thesis: for s1, s2 being FinSequence st len s1 = n & len s2 = n holds
<*s1,s2*> is tabular
let s1, s2 be FinSequence; :: thesis: ( len s1 = n & len s2 = n implies <*s1,s2*> is tabular )
assume A1: ( len s1 = n & len s2 = n ) ; :: thesis: <*s1,s2*> is tabular
take n ; :: according to MATRIX_0:def 1 :: thesis: for x being object st x in rng <*s1,s2*> holds
ex s being FinSequence st
( s = x & len s = n )
let x be object ; :: thesis: ( x in rng <*s1,s2*> implies ex s being FinSequence st
( s = x & len s = n ) )
assume x in rng <*s1,s2*> ; :: thesis: ex s being FinSequence st
( s = x & len s = n )
then A2: x in {s1,s2} by FINSEQ_2:127;
then reconsider r = x as FinSequence by TARSKI:def 2;
take r ; :: thesis: ( r = x & len r = n )
thus ( x = r & len r = n ) by A1, A2, TARSKI:def 2; :: thesis: verum