Section Test.
Variable x : nat.
Definition addx y := y + x.
wlog H : (n0 := n) (y := x) (@twoy := (id _ as X in _ <= X)) / twoy = 2 * y.
myadmit.
myadmit.
Qed.
Definition twox := x + x.
Definition bis := twox.
wlog H : (y := x) (@twoy := (X in _ <= X)) / twoy = 2 * y.
match goal with
|- (forall y : nat,
let twoy := y + y in
twoy = 2 * y -> is_true(n + y <= twoy)) ->
is_true(n + x <= twox) => myadmit end.
Restart.
wlog H : (y := x) (@twoy := (id _ as X in _ <= X)) / twoy = 2 * y.
match goal with
|- (forall y : nat,
let twoy := twox in
twoy = 2 * y -> is_true(n + y <= twoy)) ->
is_true(n + x <= twox) => myadmit end.
myadmit.
Qed.
End Test.

Lemma test_in n k (def_k : k = 0) (ngtk : k < n) : P n.