Field structure on the multiplicative opposite #
@[protected, instance]
Equations
- mul_opposite.division_ring α = {add := ring.add (mul_opposite.ring α), add_assoc := _, zero := group_with_zero.zero (mul_opposite.group_with_zero α), zero_add := _, add_zero := _, nsmul := ring.nsmul (mul_opposite.ring α), nsmul_zero' := _, nsmul_succ' := _, neg := ring.neg (mul_opposite.ring α), sub := ring.sub (mul_opposite.ring α), sub_eq_add_neg := _, zsmul := ring.zsmul (mul_opposite.ring α), zsmul_zero' := _, zsmul_succ' := _, zsmul_neg' := _, add_left_neg := _, add_comm := _, mul := group_with_zero.mul (mul_opposite.group_with_zero α), mul_assoc := _, one := group_with_zero.one (mul_opposite.group_with_zero α), one_mul := _, mul_one := _, npow := group_with_zero.npow (mul_opposite.group_with_zero α), npow_zero' := _, npow_succ' := _, left_distrib := _, right_distrib := _, inv := group_with_zero.inv (mul_opposite.group_with_zero α), div := group_with_zero.div (mul_opposite.group_with_zero α), div_eq_mul_inv := _, zpow := group_with_zero.zpow (mul_opposite.group_with_zero α), zpow_zero' := _, zpow_succ' := _, zpow_neg' := _, exists_pair_ne := _, mul_inv_cancel := _, inv_zero := _}
@[protected, instance]
Equations
- mul_opposite.field α = {add := division_ring.add (mul_opposite.division_ring α), add_assoc := _, zero := division_ring.zero (mul_opposite.division_ring α), zero_add := _, add_zero := _, nsmul := division_ring.nsmul (mul_opposite.division_ring α), nsmul_zero' := _, nsmul_succ' := _, neg := division_ring.neg (mul_opposite.division_ring α), sub := division_ring.sub (mul_opposite.division_ring α), sub_eq_add_neg := _, zsmul := division_ring.zsmul (mul_opposite.division_ring α), zsmul_zero' := _, zsmul_succ' := _, zsmul_neg' := _, add_left_neg := _, add_comm := _, mul := division_ring.mul (mul_opposite.division_ring α), mul_assoc := _, one := division_ring.one (mul_opposite.division_ring α), one_mul := _, mul_one := _, npow := division_ring.npow (mul_opposite.division_ring α), npow_zero' := _, npow_succ' := _, left_distrib := _, right_distrib := _, mul_comm := _, inv := division_ring.inv (mul_opposite.division_ring α), div := division_ring.div (mul_opposite.division_ring α), div_eq_mul_inv := _, zpow := division_ring.zpow (mul_opposite.division_ring α), zpow_zero' := _, zpow_succ' := _, zpow_neg' := _, exists_pair_ne := _, mul_inv_cancel := _, inv_zero := _}