let GF be Graph-yielding Function; :: thesis: ( GF is _trivial implies GF is connected )
assume A1: GF is _trivial ; :: thesis: GF is connected
let x be object ; :: according to GLIB_002:def 12 :: thesis: ( x in dom GF implies ex G being _Graph st
( GF . x = G & G is connected ) )
assume x in dom GF ; :: thesis: ex G being _Graph st
( GF . x = G & G is connected )
then consider G being _Graph such that
A2: ( GF . x = G & G is _trivial ) by A1, GLIB_000:def 60;
take G ; :: thesis: ( GF . x = G & G is connected )
thus ( GF . x = G & G is connected ) by A2; :: thesis: verum