Theorems · Theorem · order theory
lt_sub_iff_add_lt
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddRightStrictMono α] {a b c : α}, a < c - b ↔ a + b < c- Cited by
- 24 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.
Cites5
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
- 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 by24
Results whose statement or proof uses this declaration.
- lt_sub_iff_add_lt'proof · cited by 14
- Set.preimage_add_const_Iioproof · cited by 9
- lt_sub_commproof · cited by 3
- iUnion_Ioc_add_zsmulproof · cited by 3
- Set.sub_mem_Ioc_iff_leftproof · cited by 3
- Real.BohrMollerup.tendsto_logGammaSeqproof · cited by 2
- Real.cos_pos_of_le_oneproof · cited by 2
- lineMap_lt_lineMap_iff_of_ltproof · cited by 2
- neg_lt_sub_iff_lt_add'proof · cited by 1
- IsLowerSet.mem_interior_of_forall_ltproof · cited by 1
- exists_irrational_btwnproof · cited by 1
- denseRange_zsmul_iff_surjectiveproof · cited by 1