Theorems · Theorem · order theory
lt_of_add_lt_add_left
∀ {α : Type u_1} [inst : Add α] [inst_1 : LT α] [AddLeftReflectLT α] {a b c : α}, a + b < a + c → b < c- Cited by
- 9 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- AddLTAddLeftReflectLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddLeftReflectLTstatement and proof · cited by 33
- ContravariantClass.elimproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_mul_leproof · cited by 10
- MeasureTheory.hasSum_integral_measureproof · cited by 4
- pos_of_lt_add_rightproof · cited by 4
- ConvexOn.exists_affine_le_of_ltproof · cited by 4
- WithBot.add_lt_add_iff_leftproof · cited by 3
- WithTop.add_lt_add_iff_leftproof · cited by 2
- AddLECancellable.lt_of_tsub_lt_tsub_left_of_leproof · cited by 2
- neg_of_add_lt_rightproof · cited by 0
- OrderedCommGroup.lt_of_add_lt_add_leftproof · cited by 0