Problem 3: Consider the special case of the stable matching problem with n machinists and n welders in which all the preferences are the same: each machinist's preference from highest to lowest are wi, W2, each welder's preferences are mi,m2, ..., Mn. Prove that in this special case there is a unique stable matching. ..., Wn, and #fis a valid index into A no greater than (OS) sand Aloj..... All is a permutation of AO.....AU: and no elements beyond index i change (for all such that iklan(A). A = AXIAL) Write the missing parts of the loop invariant Prove that the inter function is correct with respect to its pre- and post-conditions using your loop invariant. You may skip the basis and induction steps for the four given parts of the marin, do the basis and induction steps for your new parts and then do the termination and postcondition parts of the proof Problem 3: Consider the special case of the stable matching problem with machinists and welders in which all the preferences are the same each machinist's preference from highest to lowest each welder's preferences are m.m.... Prove that in this special case there is a unique stable matching roblem. Consider the special case of the stable matching problem with a machinists and welders in which all the preferences are the same each machinist's preference from highest to lowest are w... Wand ach welder's that there is a stable Problem 3: Consider the special case of the stable matching problem with n machinists and n welders in which all the preferences are the same: each machinist's preference from highest to lowest are W7,W2,...,Wn, and each welder's preferences are m1,m2,..., mn. Prove that in this special case there is a unique stable matching