Theorems · Theorem · order theory
le_sub_iff_add_le
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddRightMono α] {a b c : α}, a ≤ c - b ↔ a + b ≤ c- Cited by
- 41 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroupLEAddRightMono
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
- AddRightMonostatement and proof · cited by 367
- neg_add_cancel_rightproof · cited by 75
- add_le_add_iff_rightproof · cited by 47
Cited by41
Results whose statement or proof uses this declaration.
- le_sub_iff_add_le'proof · cited by 23
- le_sub_commproof · cited by 14
- Set.preimage_add_const_Iicproof · cited by 7
- Real.log_le_sub_one_of_posproof · cited by 5
- Real.pi_upper_bound_startproof · cited by 5
- neg_le_sub_iff_le_addproof · cited by 4
- LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iffproof · cited by 3
- existsUnique_add_zsmul_mem_Icoproof · cited by 3
- existsUnique_sub_zsmul_mem_Icoproof · cited by 3
- Set.sub_mem_Ico_iff_leftproof · cited by 3
- lineMap_le_lineMap_iff_of_ltproof · cited by 2
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2