let BL be Boolean Lattice; :: thesis: for b being Element of BL
for B being Finite_Subset of the carrier of BL holds FinJoin ((B \/ {.b.}),(comp BL)) = (FinJoin (B,(comp BL))) "\/" (b `)
let b be Element of BL; :: thesis: for B being Finite_Subset of the carrier of BL holds FinJoin ((B \/ {.b.}),(comp BL)) = (FinJoin (B,(comp BL))) "\/" (b `)
let B be Finite_Subset of the carrier of BL; :: thesis: FinJoin ((B \/ {.b.}),(comp BL)) = (FinJoin (B,(comp BL))) "\/" (b `)
thus FinJoin ((B \/ {.b.}),(comp BL)) = (FinJoin (B,(comp BL))) "\/" ((comp BL) . b) by Th20
.= (FinJoin (B,(comp BL))) "\/" (b `) by Def17 ; :: thesis: verum