Theorems · Theorem · order theory
add_lt_add_iff_right
∀ {α : Type u_1} [inst : Add α] [inst_1 : LT α] [AddRightStrictMono α] [AddRightReflectLT α] (a : α) {b c : α},
b + a < c + a ↔ b < c- Cited by
- 42 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.swapproof · cited by 216
- AddRightStrictMonostatement and proof · cited by 160
- AddRightReflectLTstatement and proof · cited by 29
- rel_iff_covproof · cited by 6
Cited by42
Results whose statement or proof uses this declaration.
- sub_posproof · cited by 147
- sub_lt_iff_lt_addproof · cited by 39
- neg_lt_neg_iffproof · cited by 39
- lt_sub_iff_add_ltproof · cited by 24
- sub_negproof · cited by 22
- sub_lt_sub_iff_rightproof · cited by 8
- lt_add_iff_pos_leftproof · cited by 8
- neg_lt_iff_pos_addproof · cited by 7
- CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'statement and proof · cited by 6
- mul_lt_mul_of_neg_rightproof · cited by 6
- mul_lt_mul_of_neg_leftproof · cited by 5
- ArchimedeanClass.min_le_mk_addproof · cited by 5