Theorems · Theorem · order theory
sub_neg
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddRightStrictMono α] {a b : α}, a - b < 0 ↔ a < bFor a - -b = a + b, see sub_neg_eq_add.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroupLTAddRightStrictMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- zero_addproof · cited by 2,366
- sub_eq_add_negproof · cited by 1,023
- AddRightStrictMonostatement and proof · cited by 160
- neg_add_cancel_rightproof · cited by 75
- add_lt_add_iff_rightproof · cited by 42
Cited by22
Results whose statement or proof uses this declaration.
- sub_lt_zeroproof · cited by 4
- round_leproof · cited by 3
- sub_inv_antitoneOn_Iioproof · cited by 2
- Real.Gamma_three_div_two_lt_oneproof · cited by 2
- eventually_nhdsWithin_sign_eq_of_deriv_posproof · cited by 2
- deriv_neg_right_of_sign_derivproof · cited by 1
- closedBall_rpow_sub_one_eq_empty_auxproof · cited by 1
- BoxIntegral.Box.dist_le_distortion_mulproof · cited by 1
- Pell.IsFundamental.mul_inv_x_lt_xproof · cited by 1
- arithGeom_strictMonoproof · cited by 1
- integral_pow_abs_sub_uIocproof · cited by 1
- Monotone.ae_hasDerivAtproof · cited by 1