let it1, it2 be Element of NAT ; :: thesis: ( it1 is_sufficiently_large_for C & ( for j being Nat st j is_sufficiently_large_for C holds
j >= it1 ) & it2 is_sufficiently_large_for C & ( for j being Nat st j is_sufficiently_large_for C holds
j >= it2 ) implies it1 = it2 )
assume that
A5: it1 is_sufficiently_large_for C and
A6: for j being Nat st j is_sufficiently_large_for C holds
j >= it1 and
A7: it2 is_sufficiently_large_for C and
A8: for j being Nat st j is_sufficiently_large_for C holds
j >= it2 ; :: thesis: it1 = it2
A9: it2 <= it1 by A5, A8;
it1 <= it2 by A6, A7;
hence it1 = it2 by A9, XXREAL_0:1; :: thesis: verum