let BL be Boolean Lattice; :: thesis: for b being Element of BL
for B being Finite_Subset of the carrier of BL holds FinMeet (B \/ {.b.}),(comp BL) = (FinMeet B,(comp BL)) "/\" (b ` )
let b be Element of BL; :: thesis: for B being Finite_Subset of the carrier of BL holds FinMeet (B \/ {.b.}),(comp BL) = (FinMeet B,(comp BL)) "/\" (b ` )
let B be Finite_Subset of the carrier of BL; :: thesis: FinMeet (B \/ {.b.}),(comp BL) = (FinMeet B,(comp BL)) "/\" (b ` )
thus FinMeet (B \/ {.b.}),(comp BL) = (FinMeet B,(comp BL)) "/\" ((comp BL) . b) by Th27
.= (FinMeet B,(comp BL)) "/\" (b ` ) by Def17 ; :: thesis: verum