Theorems · Theorem · order theory
WithTop.add_lt_add_right
∀ {α : Type u} [inst : Add α] {x y z : WithTop α} [inst_1 : LT α] [AddRightStrictMono α], z ≠ ⊤ → x < y → x + z < y + z- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- AddLTAddRightStrictMono
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.
- Top.topstatement and proof · cited by 9,680
- WithTopstatement and proof · cited by 3,754
- WithTop.someproof · cited by 1,128
- AddRightStrictMonostatement and proof · cited by 160
- WithTop.recTopCoeproof · cited by 107
- add_lt_add_leftproof · cited by 47
Cited by5
Results whose statement or proof uses this declaration.
- ENNReal.add_lt_add_rightproof · cited by 2
- WithTop.add_lt_addproof · cited by 2
- WithTop.add_lt_add_iff_rightproof · cited by 2
- WithTop.add_lt_add_of_lt_of_leproof · cited by 2
- Nat.emultiplicity_two_factorial_ltproof · cited by 0