Theorems · Theorem · order theory
sub_le_sub_iff_left
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] [AddRightMono α] {b c : α} (a : α),
a - b ≤ a - c ↔ c ≤ b- Cited by
- 8 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- neg_add_cancel_leftproof · cited by 84
- neg_le_neg_iffproof · cited by 57
- add_le_add_iff_leftproof · cited by 45
Cited by9
Results whose statement or proof uses this declaration.
- sub_le_sub_leftproof · cited by 43
- OrderIso.subLeftproof · cited by 4
- SimpleGraph.triangle_counting'proof · cited by 1
- toIocMod_le_toIcoMod_addproof · cited by 0
- Int.fract_add_fract_leproof · cited by 0
- Int.fract_add_leproof · cited by 0
- toIcoMod_le_toIocModproof · cited by 0