fixpoint "--rewrite"

data Peano 0 = [ 
  | Zero {}
  | S {prev : Peano} 
  ]

constant even : (func(0, [Peano; bool]))


define even (x:Peano) : bool = {
  if (is$Zero x) then true else 
  ~ (even (prev n))
}


match is$Zero Zero = (true)
match is$Zero S x = (false)
match is$S Zero = (false)
match is$S S x = (true)
match prev S x = (x)

bind 0 n : {v: Peano | even v && is$S v && prev v == d } 
bind 1 d : {v: Peano | true  } 
bind 2 z : {v: Peano | is$Zero v && v == d } 

constraint:
  env [0; 1; 2]
  lhs {v : bool | true }
  rhs {v : bool | false }
  id 1 tag []

expand [1 : True]