RingLawArgs

forall (Scalar : Sort u), forall (zero : Scalar), forall (one : Scalar), forall (add : forall (a : Scalar), forall (b : Scalar), Scalar), forall (neg : forall (a : Scalar), Scalar), forall (sub : forall (a : Scalar), forall (b : Scalar), Scalar), forall (mul : forall (a : Scalar), forall (b : Scalar), Scalar), Prop

fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => forall (P : Prop), forall (mk : forall (sub_eq_add_neg_law : forall (a : Scalar), forall (b : Scalar), @Eq.{u} Scalar (sub a b) (add a (neg b))), forall (add_assoc_law : forall (a : Scalar), forall (b : Scalar), forall (c : Scalar), @Eq.{u} Scalar (add (add a b) c) (add a (add b c))), forall (add_comm_law : forall (a : Scalar), forall (b : Scalar), @Eq.{u} Scalar (add a b) (add b a)), forall (add_zero_law : forall (a : Scalar), @Eq.{u} Scalar (add a zero) a), forall (zero_add_law : forall (a : Scalar), @Eq.{u} Scalar (add zero a) a), forall (neg_add_cancel_law : forall (a : Scalar), @Eq.{u} Scalar (add (neg a) a) zero), forall (add_neg_cancel_law : forall (a : Scalar), @Eq.{u} Scalar (add a (neg a)) zero), forall (sub_self_law : forall (a : Scalar), @Eq.{u} Scalar (sub a a) zero), forall (mul_assoc_law : forall (a : Scalar), forall (b : Scalar), forall (c : Scalar), @Eq.{u} Scalar (mul (mul a b) c) (mul a (mul b c))), forall (mul_comm_law : forall (a : Scalar), forall (b : Scalar), @Eq.{u} Scalar (mul a b) (mul b a)), forall (mul_one_law : forall (a : Scalar), @Eq.{u} Scalar (mul a one) a), forall (one_mul_law : forall (a : Scalar), @Eq.{u} Scalar (mul one a) a), forall (left_distrib_law : forall (a : Scalar), forall (b : Scalar), forall (c : Scalar), @Eq.{u} Scalar (mul a (add b c)) (add (mul a b) (mul a c))), forall (right_distrib_law : forall (a : Scalar), forall (b : Scalar), forall (c : Scalar), @Eq.{u} Scalar (mul (add a b) c) (add (mul a c) (mul b c))), forall (mul_zero_law : forall (a : Scalar), @Eq.{u} Scalar (mul a zero) zero), forall (zero_mul_law : forall (a : Scalar), @Eq.{u} Scalar (mul zero a) zero), forall (add_left_cancel_law : forall (a : Scalar), forall (b : Scalar), forall (c : Scalar), forall (h : @Eq.{u} Scalar (add a b) (add a c)), @Eq.{u} Scalar b c), forall (ring_normalize_add_mul3_law : forall (a : Scalar), forall (b : Scalar), forall (c : Scalar), @Eq.{u} Scalar (add (add (mul a b) (mul b c)) (mul a c)) (add (add (mul a b) (mul a c)) (mul b c))), forall (add_right_cancel_law : forall (a : Scalar), forall (b : Scalar), forall (c : Scalar), forall (h : @Eq.{u} Scalar (add b a) (add c a)), @Eq.{u} Scalar b c), forall (neg_neg_law : forall (a : Scalar), @Eq.{u} Scalar (neg (neg a)) a), forall (sub_zero_law : forall (a : Scalar), @Eq.{u} Scalar (sub a zero) a), forall (zero_sub_law : forall (a : Scalar), @Eq.{u} Scalar (sub zero a) (neg a)), forall (sub_add_cancel_law : forall (a : Scalar), forall (b : Scalar), @Eq.{u} Scalar (add (sub a b) b) a), forall (add_sub_cancel_law : forall (a : Scalar), forall (b : Scalar), @Eq.{u} Scalar (sub (add a b) b) a), forall (sub_add_sub_cancel_law : forall (a : Scalar), forall (b : Scalar), forall (c : Scalar), @Eq.{u} Scalar (sub (sub a c) (sub b c)) (sub a b)), P), P