x = readInt() #PREMISES FOR ATTACHED PROOF, IF ANY: # True #PREMISES FOR NEXT LINE: y = readInt() #PREMISES FOR ATTACHED PROOF, IF ANY: # True #PREMISES FOR NEXT LINE: assert y > x #PREMISES FOR NEXT LINE: # (y > x) """{ 1.OK y > x premise }""" #PREMISES FOR NEXT LINE: # (y > x) x = x - 1 #PREMISES FOR ATTACHED PROOF, IF ANY: # (x == (x_old - 1)) # (y > x_old) """{ 1.OK y > x_old premise 2.OK x == x_old - 1 premise 3.OK x_old == x + 1 algebra 2 # The checker will manipulate line 2 into line 3. 4.OK y > x + 1 subst 3 1 # subst the equality on line 3 into formula on line 1. # This eliminates x_old from the knowlege carried forwards. }""" #PREMISES FOR NEXT LINE: # (y > (x + 1)) y = y + 1 #PREMISES FOR ATTACHED PROOF, IF ANY: # (y == (y_old + 1)) # (y_old > (x + 1)) """{ 1.OK y_old > x + 1 premise 2.OK y == y_old + 1 premise 3.OK y > x algebra 1 2 # The checker will deduce these steps for you: # y_old == y - 1 # y - 1 > x + 1 # y > x + 2 }""" #PREMISES FOR NEXT LINE: # (y > x)