Theorems · Theorem · order theory
WithTop.add_lt_add_left
∀ {α : Type u} [inst : Add α] {x y z : WithTop α} [inst_1 : LT α] [AddLeftStrictMono α], x ≠ ⊤ → y < z → x + y < x + z- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- AddLTAddLeftStrictMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddLeftStrictMonostatement and proof · cited by 203
- WithTop.recTopCoeproof · cited by 107
- add_lt_add_rightproof · cited by 50
- WithTop.add_topproof · cited by 18
Cited by4
Results whose statement or proof uses this declaration.
- ENNReal.add_lt_add_leftproof · cited by 4
- WithTop.add_lt_addproof · cited by 2
- WithTop.add_lt_add_iff_leftproof · cited by 2
- WithTop.add_lt_add_of_le_of_ltproof · cited by 2