Theorems · Theorem · order theory
WithBot.add_lt_add_of_le_of_lt
∀ {α : Type u} [inst : Add α] {w x y z : WithBot α} [inst_1 : Preorder α] [AddLeftStrictMono α] [AddRightMono α],
w ≠ ⊥ → w ≤ y → x < z → w + x < y + z- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Bot.botstatement and proof · cited by 4,720
- WithBotstatement and proof · cited by 1,498
- LT.lt.trans_leproof · cited by 678
- AddRightMonostatement and proof · cited by 367
- AddLeftStrictMonostatement and proof · cited by 203
- add_le_add_leftproof · cited by 37
- WithBot.add_lt_add_leftproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.