(* TODO do implicits for the rest of the file *)
Set Implicit Arguments.
Unset Strict Implicit.

(* Specifications: *)
Lemma lt0_False :
forall n, ~ n < 0.
Lemma leq_ltS n m :
n <= m -> n < m.+1.
Lemma ltS_leq n m :
n <= m -> n < m.+1.
Lemma plus_leq_compat_l n m k :
n <= m ->
n <= m + k.
Lemma plus_leq_compat_r n m k :
n <= k ->
n <= m + k.
Lemma leq_refl: forall n, n <= n.
Lemma succ_neq_zero :
forall x, S x <> 0.
Lemma isSomeSome {A : Type} (y : A) :
Some y.
Lemma eq_symm {A : Type} (x y : A) :
x = y -> y = x.
Lemma ltn0Sn_pair {A : Type} (n : nat) (g : A)  :
0 < (n.+1, g).1.