intuition.
Qed.

(* Specifications: *)
Lemma lognat_ge_monotonic_h : forall (c a b : nat)(pfa : a <> 0)(pfb : b <> 0),
a >= b -> c = (a - b) -> (lognat pfa) >= (lognat pfb).
Lemma lognat_ge_monotonic_mt : forall (a b : nat)(pfa : a <> 0)(pfb : b <> 0),
(lognat pfa) < (lognat pfb) -> a < b.
Theorem app_eq_inv :
forall (A : Type)(ls1 ls2 ls3 ls4 : list A),
length ls1 = length ls3 ->
(ls1 ++ ls2) = (ls3 ++ ls4) ->
ls1 = ls3 /\ ls2 = ls4.
Theorem sumList_1_mult :
forall (A : Set)(ls : list A),
sumList ls (fun _ => 1) == length ls / 1.
Lemma plus_eq_compat : forall n1 n2 n3 n4,
n1 = n2 ->
n3 = n4 ->
n1 + n3 = n2 + n4.
Lemma minus_diag_eq : forall n1 n2,
n1 = n2 ->
n1 - n2 = 0.
Lemma le_eq : forall n1 n2,
n1 = n2 ->
n1 <= n2.
Lemma minus_add_assoc : forall n1 n2 n3,
(n3 <= n2)%nat ->
(n1 + (n2 - n3) = n1 + n2 - n3)%nat.
Lemma bleRat_total : forall r1 r2,
bleRat r1 r2 = false -> bleRat r2 r1 = true.
Theorem ratSubtract_le : forall r1 r2 d,
r1 <= d ->
ratSubtract r1 r2 <= d.
Lemma ratSubtract_ratAdd_assoc: forall r1 r2 r3,
r3 <= r2 ->
ratSubtract (r1 + r2) r3 == r1 + (ratSubtract r2 r3).
Theorem list_inhabited :
forall (A : Set), list A.
Lemma app_first_eq : forall (A : Type)(ls2 ls1 ls3 : list A),
ls1 = ls2 ++ ls3 ->
length ls1 = length ls2 ->
ls1 = ls2 /\ ls3 = nil.