Theorems · Theorem · order theory
le_or_lt_of_add_le_add
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : Add α] [AddLeftMono α] [AddRightStrictMono α] {a₁ a₂ b₁ b₂ : α},
a₁ + b₁ ≤ a₂ + b₂ → a₁ ≤ a₂ ∨ b₁ < b₂- Cited by
- 3 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.
Cites6
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
- AddLeftMonostatement and proof · cited by 687
- not_leproof · cited by 328
- not_ltproof · cited by 306
- AddRightStrictMonostatement and proof · cited by 160
- add_lt_add_of_lt_of_leproof · cited by 37
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.IsHomogeneous.isPrime_of_homogeneous_mem_or_memproof · cited by 3
- cauchy_davenport_minOrder_addproof · cited by 2
- cauchy_davenport_minOrder_mulproof · cited by 1