Theorems · Theorem · order theory
le_add_iff_lt_left_or_exists_le
∀ {α : Type u_1} [inst : LinearOrder α] {a b c : α} [inst_1 : Add α] [CanonicallyOrderedAdd α] [AddLeftMono α]
[IsLeftCancelAdd α], a ≤ b + c ↔ a < b ∨ ∃ d ≤ c, a = b + d- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- AddLeftMonostatement and proof · cited by 687
- CanonicallyOrderedAddstatement and proof · cited by 229
- lt_or_geproof · cited by 182
- IsLeftCancelAddstatement and proof · cited by 72
- le_self_addproof · cited by 68
- ExistsAddOfLE.exists_add_of_leproof · cited by 42
Cited by1
Results whose statement or proof uses this declaration.
- le_add_iff_lt_right_or_exists_leproof · cited by 0