Theorems · Theorem · order theory
add_le_add_iff_of_ge
∀ {α : Type u_1} [inst : Add α] [inst_1 : PartialOrder α] [AddLeftStrictMono α] [AddRightStrictMono α]
{a₁ a₂ b₁ b₂ : α}, a₁ ≤ a₂ → b₁ ≤ b₂ → (a₂ + b₂ ≤ a₁ + b₁ ↔ a₁ = a₂ ∧ b₁ = b₂)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- le_reflproof · cited by 2,061
- AddLeftMonoproof · cited by 687
- AddRightMonoproof · cited by 367
- AddLeftStrictMonostatement and proof · cited by 203
- LE.le.not_gtproof · cited by 189
- AddRightStrictMonostatement and proof · cited by 160
- add_lt_add_of_lt_of_leproof · cited by 37
- add_lt_add_of_le_of_ltproof · cited by 31
- eq_iff_le_not_ltproof · cited by 11
- addLeftMono_of_addLeftStrictMonoproof · cited by 10
- addRightMono_of_addRightStrictMonoproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- add_eq_add_iff_eq_and_eqproof · cited by 3
- NonemptyInterval.add_eq_zero_iffproof · cited by 1