let C be non empty set ; :: thesis: for f, g, h being Membership_Func of C holds f \ (g \ h) = max (f \ g),(min f,h)
let f, g, h be Membership_Func of C; :: thesis: f \ (g \ h) = max (f \ g),(min f,h)
f \ (g \ h) =
min f,(max (1_minus g),(1_minus (1_minus h)))
by FUZZY_1:12
.=
max (min f,(1_minus g)),(min f,h)
by FUZZY_1:10
;
hence
f \ (g \ h) = max (f \ g),(min f,h)
; :: thesis: verum