le_S: forall n m : nat, n <= m -> n <= S m
le_n: forall n : nat, n <= n
false: bool
true: bool
sumor_beq:
  forall (A : Type) (B : Prop),
  (A -> A -> bool) -> (B -> B -> bool) -> A + {B} -> A + {B} -> bool
sumbool_beq:
  forall A B : Prop,
  (A -> A -> bool) -> (B -> B -> bool) -> {A} + {B} -> {A} + {B} -> bool
xorb: bool -> bool -> bool
sum_beq:
  forall A B : Type,
  (A -> A -> bool) -> (B -> B -> bool) -> A + B -> A + B -> bool
prod_beq:
  forall A B : Type,
  (A -> A -> bool) -> (B -> B -> bool) -> A * B -> A * B -> bool
orb: bool -> bool -> bool
option_beq: forall A : Type, (A -> A -> bool) -> option A -> option A -> bool
negb: bool -> bool
nat_beq: nat -> nat -> bool
list_beq: forall A : Type, (A -> A -> bool) -> list A -> list A -> bool
implb: bool -> bool -> bool
comparison_beq: comparison -> comparison -> bool
bool_beq: bool -> bool -> bool
andb: bool -> bool -> bool
Empty_set_beq: Empty_set -> Empty_set -> bool
pred_Sn: forall n : nat, n = pred (S n)
plus_n_Sm: forall n m : nat, S (n + m) = n + S m
plus_n_O: forall n : nat, n = n + 0
plus_Sn_m: forall n m : nat, S n + m = S (n + m)
plus_O_n: forall n : nat, 0 + n = n
mult_n_Sm: forall n m : nat, n * m + n = n * S m
mult_n_O: forall n : nat, 0 = n * 0
eq_add_S: forall n m : nat, S n = S m -> n = m
eq_S: forall x y : nat, x = y -> S x = S y