#lang ivy1.7

schema exi = {
    type t
    function p(X:t) : bool
    function witness : t
    property p(witness)
    #-------------------
    property exists Y. p(Y)
}

theorem refl = {
    type t
    property X:t = X
}

type q
var z : q

property [foo] z = z
proof apply refl

type t1
var v1 : t1

property exists X:t1. X = v1
proof apply exi<foo/witness,t2/t> with foo = v1; apply refl