hereby :: thesis: ( ( for x being Nat holds GSq . x is _finite ) implies GSq is _finite )

assume A1: GSq is _finite ; :: thesis: for x being Nat holds GSq . x is _finite
let x be Nat; :: thesis: GSq . x is _finite
x in dom GSq by LmNat;
hence GSq . x is _finite by A1; :: thesis: verum

end;

assume A2: for x being Nat holds GSq . x is _finite ; :: thesis: GSq is _finite
let x be Element of dom GSq; :: according to GLIB_000:def 66 :: thesis: GSq . x is _finite
thus GSq . x is _finite by A2; :: thesis: verum