let a, b, s, t be complex number ; :: thesis: {a,b} ** {s,t} = {(a * s),(a * t),(b * s),(b * t)}
thus {a,b} ** {s,t} =
({a} \/ {b}) ** {s,t}
by ENUMSET1:41
.=
({a} ** {s,t}) \/ ({b} ** {s,t})
by Th98
.=
{(a * s),(a * t)} \/ ({b} ** {s,t})
by Th105
.=
{(a * s),(a * t)} \/ {(b * s),(b * t)}
by Th105
.=
{(a * s),(a * t),(b * s),(b * t)}
by ENUMSET1:45
; :: thesis: verum