let C be non empty set ; :: thesis: for f, h, g being Membership_Func of C holds f \ (min (g,h)) = max ((f \ g),(f \ h))
let f, h, g be Membership_Func of C; :: thesis: f \ (min (g,h)) = max ((f \ g),(f \ h))
thus f \ (min (g,h)) = min (f,(max ((1_minus g),(1_minus h)))) by FUZZY_1:11
.= max ((f \ g),(f \ h)) by FUZZY_1:9 ; :: thesis: verum