let G be non empty join-commutative join-associative Robbins ComplLLattStr ; for x being Element of G holds \delta (((x _1) + (x _3)),x) = x _0
let x be Element of G; \delta (((x _1) + (x _3)),x) = x _0
x _0 =
Expand ((x _4),(x _0))
by Th36
.=
\delta (((x _4) + (x _0)),(\delta ((x _4),(\delta ((x _3),x)))))
by Th48
.=
\delta (((x _3) + (x _1)),(\delta ((x _4),(\delta ((x _3),x)))))
by Th42
.=
\delta (((x _3) + (x _1)),(Expand ((x _3),x)))
by Th44
.=
\delta (((x _3) + (x _1)),x)
by Th36
;
hence
\delta (((x _1) + (x _3)),x) = x _0
; verum