Theorems · Theorem · order theory
add_lt_add_left
∀ {α : Type u_1} [inst : Add α] [inst_1 : LT α] [i : AddRightStrictMono α] {b c : α}, b < c → ∀ (a : α), b + a < c + a- Cited by
- 47 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- AddLTAddRightStrictMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddRightStrictMonostatement and proof · cited by 160
- CovariantClass.elimproof · cited by 22
Cited by47
Results whose statement or proof uses this declaration.
- add_lt_add_of_lt_of_leproof · cited by 37
- lt_add_of_pos_leftproof · cited by 19
- add_lt_add_of_lt_of_ltproof · cited by 13
- Metric.ball_subset_ball'proof · cited by 7
- lt_add_of_pos_of_leproof · cited by 6
- StrictMono.add_constproof · cited by 6
- WithTop.add_lt_add_rightproof · cited by 5
- Polynomial.coeff_mirrorproof · cited by 4
- trichotomy_of_add_eq_addproof · cited by 3
- StrictConvexOn.map_sum_ltproof · cited by 3
- starConvex_compl_Iicproof · cited by 2
- add_lt_of_neg_leftproof · cited by 2