elim-dep-00.fq

qualif False(v:int) : (0 = 1)
qualif Zero(v:int) : (0 = v)
qualif One(v:int) : (1 = v)

bind 1 x : {v:int | $k2 }

// cut $k1 -- eliminating $k1 causes UNSOUNDNESS

cut $k2


constraint:
  env [ ]
  lhs {v : int | v = 0 }
  rhs {v : int | $k1   }
  id 1 tag []

constraint:
  env [ 1 ]
  lhs {v : int | v = x + 1 }
  rhs {v : int | $k1       }
  id 2 tag []

constraint:
  env [ ]
  lhs {v : int | $k1}
  rhs {v : int | $k2}
  id 3 tag []

constraint:
  env [ ]
  lhs {v : int | $k2  }
  rhs {v : int | 0 = v}
  id 4 tag []

wf:
  env [ ]
  reft {v: int | $k1}

wf:
  env [ ]
  reft {v: int | $k2}