```

#PREMISES FOR ATTACHED PROOF, IF ANY:
# True
#PREMISES FOR NEXT LINE:
#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)
```