Please explain the proofs of these formula, I am very confused and I am not understanding this, what does all the eg b means?

Proof that the rigid wage is equal to the expected wage We want to find out how the average wage level is determined. To do this, we first find the flexible wage and then the rigid wage, and then we combine them. The flexible wage (relative to the lagged wage) is determined by the average wage increase and the actual rate of unemployment: A Wx AW. - b (u - u" ) . Inserting the expression for the average wage increase in this expression, we get A Wx A Wx A WT + (1-2) t - b(u, - u") . We now solve for the increase in the flexible wage: A WX A W. b (14, - u") . 1- 2The rigid wage is set according to the wage-setting equation but based on expec- tations at the end of the previous period about the average wage level and the unemployment rate: AW: AW _ b(u; - 1"). The rigid wage setters know the rigid wage and using the equation above to form expectations about the flexible wage increase we get AWN AW: b WH1 1- 2 (4, - 2") . Thus we get AW! AW! b WE - 1-x (4; -10") + (1-2) AW - blu - 1"). Comparing the left- and the right-hand sides, we see that the terms involving AW!/W. , cancel out, so the only way this equality can hold is if u' = u". Thus we see that, in this simple model, the rigid wages are set in such a way that unem- ployment is expected to be at the natural level. This result is intuitive. If wages were set so that unemployment would be expected to be lower than the natural level, firms would have incentives to raise wages. For firms to be content with their wage decision, the rigid wage must be such that unemployment is expected to be on its natural level. Then the equation for the rigid wage above implies AW! AW _ b(u; - u") = AW: This condition is used in the text to solve for the average wage increase