Theorems · Theorem · order theory
trichotomy_of_add_eq_add
∀ {α : Type u_1} [inst : Add α] [inst_1 : LinearOrder α] {a b c d : α} [AddLeftStrictMono α] [AddRightStrictMono α],
a + b = c + d → a = c ∧ b = d ∨ a < c ∨ b < d- Cited by
- 3 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.
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_totalproof · cited by 294
- ne_of_ltproof · cited by 203
- AddLeftStrictMonostatement and proof · cited by 203
- lt_trichotomyproof · cited by 178
- AddRightStrictMonostatement and proof · cited by 160
- add_lt_add_leftproof · cited by 47
- add_lt_add_of_lt_of_ltproof · cited by 13
- add_right_inj_of_comparableproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.order_mulproof · cited by 2
- MvPowerSeries.weightedHomogeneousComponent_mul_of_le_weightedOrderproof · cited by 2
- MvPowerSeries.coeff_mul_of_add_lexOrderproof · cited by 1