# this proof relies heavily on the checker tool's calculations:
if x > y :
    #PREMISES FOR THEN-ARM: 
    # (x > y)
    max = x
    #PREMISES FOR ATTACHED PROOF, IF ANY: 
    # (max == x)
    # (x > y)
    #PREMISES FOR NEXT LINE: 
    # (max == x)
    # (x > y)
else :
    #PREMISES FOR ELSE-ARM: 
    # not (x > y)
    max = y 
    #PREMISES FOR ATTACHED PROOF, IF ANY: 
    # (max == y)
    # not (x > y)
    #PREMISES FOR NEXT LINE: 
    # (max == y)
    # not (x > y)
#PREMISES FOR NEXT LINE: 
# (((max == x) and (x > y)) or ((max == y) and not (x > y)))

"""{ 1.OK ((max == x) and (x > y)) or ((max == y) and not (x > y))     premise
     2.OK max >= x                                                     ore 1
     3.OK max >= y                                                     ore 1
     4.OK max >= x  and  max >= y                                      andi 2 3
}"""
#PREMISES FOR NEXT LINE: 
# ((max >= x) and (max >= y))